I'd agree with all the suggestions above. Then consider what the E-class owner's bible says:

"All E-class

Rumbling/humming in speed range from 110--150 kph.

Driveshaft out of balance. Balance driveshaft. If problem persists, install rear differential vibration damper (124 350 03 72) at rear subframe. Tightening torque 150 Nm."

My mechanic reckons an out-of-balance driveshaft is very distinctive and therefore easy to diagnose. In the case of my E320 Coupé we fitted the damper -- a heavy lump of easily fitted metal -- which had some effect but has not eliminated the problem entirely. Now I have a centre bearing to replace.