My best guess so far is a 1950's or earlier stereo headphone line amplifier.
There are three holes in the unit, all visible in the second shot. Two are for the 1/4 stereo jacks, and a small one on the right allows access to an adjustment screw on the lower silver box. The triangle stamped on this box has a single E in it.
The writing you can see in the second shot is "4.5 V + -", indicating three dry cells attatched to the screw points to provide power. There's room for C cells.