where U is the total internal energy of the particle, ie. U = E, and this is indeed true for a massless particle.
E = pc also comes from Einstein's equation. The actual equation derived by Einstein is
If the particle is massless we have E = pc like we had above. If the particle is at rest (ie. no momentum) we get the celebrated .
I cannot think where the Maxwell equation would be found, but Maxwell's work in this case is for bosons (subatomic particles with integer spins) and probably would be found under a search on spin-statistics correlations. You can find a derivation of Einstein's equation in just about any Modern Physics text. That will give you a starting point anyway.