State Einsiein's equation of photoelectric effect and what conservation principle does Einstein's equation represent

Einsteins equation of photoelectric effect can be stated in many ways, however I suspect the one you're seeking is:

hf = Φ + E kmax

The Ekmax part is important because only electrons at the surface will have the maximum KE on leaving, some will need to use some of the hf (energy supplied from the photon) to get to the surface of the metal first. Phi relates to the energy the electrons use to escape the surface, what he called the work function.

This is an equation that relates fundamentally to the Conservation of Energy, because the energy supplied by the photon is equal to the energy the electron used to escape combined with the max KE of the electrons escaping. In other words, the energy going in is equal to the energy going out, which conforms to the fact Energy can only be transformed and transferred.