the chord your looking for is Bm, true it's not in key, but that's how it goes. You'll play 2 measures on Emaj7-X79897, then 2 measures on Bm-XX9777.
Sometimes you can slip a higher A barre in there-XX7655. when adding this you'll do 2 measures on Emaj7, 1 measure on Bm, then 1 measure on A.
before you go back into the verses you'l switch the Bm to a major. i.e. 1 measure on Emaj7, half a measue on B, half a measure on A.
if you want to solo on it, try playing in E while playing the Emaj7 and swith to A while the Bm is playing, it sounds really great when you get it to work.
Good luck, have fun.
your cosmic brother