I taught myself systems engineering, computer science, electrical engineering, and some chemistry. Most of these, I taught myself with low amount of investment, pirated books, pirated software, and garbage salvage.
I now work for the federal govt as a contractor making $150k/yr. The classes I took never even remotely got me here. I got me here.
Start looking at what the basic parts are. Look up spec sheets. Figure them out and what they mean. You may know what you want to do, but finding the part is half this battle. Start figuring out what the landscape looks like. Last you want to do is design something with retired status and no NOS (new old stock).
Also start getting electronic books on the basic topics. Trawl through college book lists, and then hit up libgen.is or other library genesis sites and get the books. We're trying to do this assuming you have very little money to work with. So piracy it is. And in actuality, the fundamentals don't really change much.
Learn analog circuitry. Go study and make your own simple circuits like circuit benders and acoustic effects.
Then dig into digital stuff. Lots of things here. You'll want to learn boolean logic, circuit analysis, and the like. There's tons of electronics to fuck around with to l;earn how they work and not work.
Past analog and digital stuffs are sensors and actuators. Sensors pick up things from the world, and actuators are things that interact with the real world. Learning and building your own 3d printer can teach you a LOT about this area in a rather quick manner. And working with an open source firmware like Merlin or Klipper can teach you digital handlings, firmware (with no OS), timing, handling analog signals, cleaning up various data, extending the hardware/software, and generally teaching yourself by trial by fire.... and print a whole lot of cool things too. (Helps to also 3d print project boxes.)
Learn how to handle power applications. Obviously we're not talking the 10kV circuits... We're talking handling batteries of various chemistries, building charge/discharge circuitry, and safe handling of the more dangerous lithium chemistries so they dont do a boeing or tesla on you. If you mess with lithiums, invest in 2 big metal buckets each half-full with sand. You'll thank me.
Get good with an IDE, like KiCAD. You'll eventually start building your own boards and parts and add them as usable things in other designs. If you get a job in industry, you'll likely use Altium. Pirate it if you can to learn it. Use the autorouter, and then do it by hand, and realize how terrible the autorouter is. Board design is just as much as an art as it is hard science. I've also heard for calculating EM prop to use something like http://openems.de/start/index.php but most tools in this realm are stupid expensive. Again, find and pirate.
Pick up some cheaper instrumentation. You'll want a good bench power supply, good 2 channel oscilloscope at 50MHz or better, signal generator, good soldering iron, good hot air rework station, fluxes, solders, solder braid, solder sucker, inspection microscope, logic analyzer, and more narrower hardware as your studies and need arise.
I also learned reverse engineering, at multiple levels. There's a lot of stuff that this can be used to attack your hardware that protects itself from, well, you. Some of the attacks are pretty simple, and others are crazy complex. Again, you might get really lucky. This usually inst taught in schools 'proper'. "Hacker skills" are usually frowned upon by the academics.
If you;re adventurous, you can also get into RF. Just be aware, this will sink your money like nothing else. A single decent SDR can easily cost you $700... And you still need a whole slew of equipment to get it to work. You can start out pretty cheaply, with 2 hackRF clones, 2 tcxo's, 2 RatLSnake antenna kits, and start learning from there. There's a lot to learn from a whole lot of fields, but even small advances are definitely noteworthy, and easily could get you published.
I know this misses quite a lot in the EE domain. However you can easily fill in the blanks as your need arises. There's a bit of analytics and mathematics I didn't directly discuss. You'll need to learn calculus. FFTs are definitely super importent and "integral" (haha) to anything regarding signals and information. https://catalog.purdue.edu/preview_program.php?catoid=7&poid... has a general listing of what their EE classes look like. You can hit wikipedia and youtube for those topics. There's LOTS of really great videos that explain the math and science online. Use those resources.
(I saved this for last, but I would also ask that you consider working on your English and grammar. Some of the worst spelling I've seen has been done by engineers. Try not to continue that trend. Lay-people and managerial/leadership types will take you more seriously.... But engineers... I don't think they'd notice :D )
