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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.
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