EdX are going to launch a Master’s degree in EE sometime in the next few months.
MIT’s OCW courses from CS&EE https://ocw.mit.edu/courses/electrical-engineering-and-compu...
Circuits and Electronics 1 (there are three)
You can take the MIT sequence of courses on edX (taught by, I believe the CEO of edX, so, in a sense, this is the original flagship edX course) https://www.edx.org/course/circuits-electronics-1-basic-circ... https://www.edx.org/course/circuits-electronics-2-amplificat... https://www.edx.org/course/circuits-electronics-3-applicatio...
I'm studying Electronics Engineering and have found this course to be a good summary of the theory essentials: https://www.edx.org/course/circuits-electronics-1-basic-circ...
For the practical side of things buy a protoboard, a multimeter and some components (resistors, capacitors, etc) and start mounting simple circuits. Learn how to solder and start fixing stuff and doing fun projects. You'll eventually need more stuff to learn, having an oscilloscope to see the signals is needed to understand what is going on with AC circuits, but you could probably simulate it instead with software like Multisim https://www.multisim.com/create/
Learn about Microcontrollers too, they give you the ability to do the really cool stuff, like robotic projects.
• MITx "Introduction to Solid State Chemistry" . I've never been good at chemistry, but this course managed to make it clear to me.
• MITx "Circuits and Electronics"  (three links because they have split it into three courses since I took it). Most electronics courses have not worked well for me. Some fail by using analogies that don't work for me. The analogies are either to things I don't understand, or to things I understand too well compared to the target audience for the course.
The latter might seem odd--how can understanding the analogous system too well cause a problem? It's because there usually isn't a perfect match between behavior of the analogous system and electronics. The more you know about the analogous system, the more likely you are to know about those places that don't match. If the author expects the students will not know about those parts, they won't mention the limitations from those parts. So you can end up expecting too much of the analogous system to apply.
Other courses have not worked for me by being too deep and detailed. For instance at one time I knew, from a solid state physics intro I took, how a semiconductor diode worked at a quantum mechanical level. I could do the math...but the course gave me no intuition for actually using the diode in a useful circuit.
The "Circuits and Electronics" course struck for me a perfect balance.
• MITx "Computation Structures" . At the end of this three part course (of which I only took the first two parts), you will know how digital logic circuits work at the transistor level, and you will know how to design combinatorial and sequential logic systems at the gate level, and you will know how to design a 32-bit RISC processor...and you will have done all those designs, using transistor level and gate level simulators.
As I said, I only took the first two parts (didn't have time for the third). In the first two parts we did cover caching and pipelining, but we didn't use them in our processor. I believe that in the third part those and other optimization are added to the processor.
• Caltech "Learning From Data" . The big selling point of this course is that it is almost the same as what Caltech students get when they take it on campus. The only watering down when I took it was the homework was multiple choice so it could be graded automatically.
The most outstanding thing about this course was Professor Abu-Mostafa's participation in the forums. He was very active answering questions. I don't know if he still does that now that the course is running in self-paced mode.
A very good start would be MIT's 6.002x via edX. It's currently offered in 3 parts, all self-paced:
Maybe you would like this:
You can just buy the microcontroller and do it yourself from there. Here is a nice example someone did of a simple LED flasher  with just 6 parts:
1. An ATmega ATTiny85 microcontroller
2. A socket for that processor
3. A coin cell battery
4. A holder for the battery
5. A resistor
6. An LED
and some wire and solder.
What going with an actual Arduino or Arduino compatible gets you, from a hardware point of view, is a bunch of ready made attachments. For instance, suppose you have some sensor that needs an odd voltage and has weird timing requirements. It will be a lot more convenient to get a shield that has that sensor, and a voltage converter, and something that deals with the weird timing and presents a simple I2C interface to your code than to have to do all that yourself.
There are some EdX courses that you might find useful.
From UTAustinX, "Embedded Systems--Shape the World" . This is a lab-based course where you do 13 or so labs using a TI Tiva Series C Launchpad. That's an 80 MHz ARM Cortex M4 board. Cost for the hardware for the course is $35-$55, depending on if you want to do a couple of the optional labs.
From UCBerkeleyX, "Electronic Interfaces: Bridging the Physical and Digital Worlds" . Another lab course
From MITx, "Circuits and Electronics" . The online version of MITs 6.002 introductory electronics course.
edX 6.002X, MIT's introductory circuits course, just started up:
I'm not aware of many more advanced EE online courses.