IANAP, but as far as I know it is true only if m is the relativistic mass which apparently is an obsolete and confusing concept which is not taught anymore (according to Wikipedia Einstein himself disliked it). Otherwise the formula only holds at rest.

It's a simplified equation which only fully applies in the case where momentum is zero.

The full equation[1] is:

    E^2 = (pc)^2 + (m0 c^2)^2

...where p is momentum, and m0 is rest mass (mass in the rest frame of the object.)

[1] https://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalenc...