  We consider non-equilibrium relaxation of electrons due to their coupling
with phonons in a simple metal. In our model electrons are living at a higher
temperature than that of the phonon bath, mimicking a non-equilibrium steady
state situation. We study the relaxation of such hot electrons proposing a
suitable generalization of the memory function formalism formulated by G\"otze
and W\"olfle[Phys. Rev. B 6, 1226 (1972)]. We derive analytical expressions for
both dc and optical scattering rates in various temperature and frequency
regimes. Limiting cases are in accord with the previous studies. An interesting
feature, that the dc scattering rate at high temperatures and optical
scattering rate at high frequencies, are independent of the temperature
difference between the electrons and the phonons is found in this study. The
present formalism forms a basis which can also be extended to study
hot-electron relaxation in more complex situations
