Is it possible to earn an electrical or computer engineering degree while remaining on active duty as an enlisted soldier?

Anything you really want you can achieve, I earned a BS and MS in Cyber Security online, there was a lot of distance lab and extra cost for me, but it was worth it all.

Anything is possible, the real problem with those particular degrees is that there is usually a significant amount of lab time associated with them. This means finding a school with the resources to finish filling in the gaps to meet certification. The education counselors at your facility are probably best suited to help you line up the combination of classes you will need with the schools in the area capable of working with you.
Most of the places I have been are pretty good about providing on base classes that answer the needs of several contracted schools in the area as well as many online education systems. The problem becomes one of time and mission requirements.

Take that long term assignment near a school you'd like to attend. Check within Corps of Engineering -- they might have some kind of academic furlough program. I think they always need engineers. Or you could take a tour in the National Guard and do OTS along the way.