I have written a song involving these two chords:
E 9 7
B 9 7
G 9 7
D 11 9
A 12 10

What scale or mode should I solo in to help preserve the kind of mellow sound of these chords.
Scream And Fly]I masturbate with it, and as an encore act, I release my spunk on people's faces. They love it
Hmm, look into the lydian scale, maybe the Ionian too.

Listen to some Vai for ideas of what the Lydian scale sounds like. For an idea of lydian in this sort of feel maybe listen to "always with me always with you" by Joe Satriani.

The Ionian scale is just the major scale which may also be nice, though a bit. . ."normal" perhaps.