I'm not that familiar with the current theoretical standing on how electrons "absorb" photons, as in the sense that electrons in an atom absorb photons and move from lower to higher energy states. But during the absorption of a photon the electron, if you set units of c=1, gains energy and therefore gains mass. Once It gains mass/energy it re-configures itself around a higher energy state. That electron absorbs the energy and then subsequently releases the energy to get back to its ground state. Could you consider the increase of energy an increase of mass of the electron? what determines the release of the photon?