Photons, no energy? If $E = mc^2$ and $m=0$

Question

I am only 14, so I don't know much about physics, and I would appreciate help on this topic.

A photon, is said to have 0 mass. However, they carry energy, as electromagnetic radiation. Albert Einstein proved that $E = mc^2$. But if you plug the data in, $E = 0\times (299791)^2$, you try to multiply the speed of light squared by $0$. Therefore, the energy of a photon would be $0$. How is that possible? Since all the photon does is carry energy?

Answer 1

The relation $E=mc^2$ only works for particles at rest, which is evidently not the case for photons. In the general case, the relation is $$E^2=m^2c^4+p^2c^2$$ for a particle with momentum $p$. (Note, though that the momentum is not necessarily $p=mv$ as in the newtonian case! See for instance If photons have no mass, how can they have momentum?)

For a massless particle, then, $E=pc$.