I think you are scrambling up Electronics Engineering and Computer Science. There is some overlap, of course, but EEs generally design hardware (products) and programmers make them useful. Even in college, there is some overlap and EEs will get some exposure to programming and CS guys will get some exposure to hardware when the discussion turns to jpw computers work.
Entrepreneur? That's going to be different, you may need to know both ends of the job. At a minimum, you need to be very good with C programming. I would think, hardware wise, you would be looking at embedded chips like the ARM processors. I don't know what kind of products you plan to build but I would bet they wind up with a microcontroller of some kind.
Want to build products based on Linux? That might involve something like a Raspberry PI and a bunch of Python code. Or C...
I'm not much on the higher level languages like Java and C++ because I don't see where they are a benefit for embedded programming. I'm probably wrong!
EE school takes about 4 years and 140 units (realistically, that can only be achieve by taking 12 units per semester, 3 semesters per year). Some of it is nonsense but the vast majority of math and science classes will be quite useful. You simply can not avoid higher level math and physics. Throw in another 30+ units for an MSEE if you think if would be useful. It can be done in a 3 semester year...
I don't know much about the CS curriculum but I did note that it takes 15 units of math starting with Calculus 1. At a minimum, it will get to Differential Equations. So, pretty deep in math. Statistics will also be a required math class.
And, lacking all of the above, you could tumble to an idea, do a lot of research on the web and come out with a product. It happens all the time. I don't know what language you will use to program but it will be called C.