Hi, I am a professional certified mechanic, with an engineering background, and 35+ years experience. I will do my best to assist you. Also keep in mind I don't know if you are a pro or a novice, so feel free to add any additional info at any time.
There were three different automatic transmissions used in the 2008 E350. If you have the 4R70W, or the 4R75W, there is nothing electrical about reverse, so the problem would have to be mechanical. It could have a bad Low/Reverse Band, or a bad Reverse clutch pack. There are some band related issues that can be fixed without removing and disassembling the transmission. But if a clutch pack has failed from wear, or a bad lip seal then it has to come out and apart. Good luck with it, have a great day, and Thanks for using Just Answer.
I do not get paid for my work unless you rate at 3 to 5 Smiley Faces or Stars, a bonus is always greatly appreciated. If the answer is not clear, let me know what additional help you need, and I will be happy to assist you further.