Okay, I hate to be pedagogic, but the moon
does emit light. Just like any object that's not at absolute zero temperature, it's a
black body, and thus radiates according to the Stefan-Boltzmann law
It does not emit
visible light, but that's a detail.
Incidentally, this implies that the earth and the moon are at roughly the same temperature (when averaged over the surface of the body). There are effects from greenhouse gases, albedo and self-heating, but solar radiation does dominate the equations. Neat!