Ok, bit of of a misnomer.
C is NOT the speed of light. C just happens to be the same speed at which light travels in a vacuum.
The C in this equation is much better thought of as "Causality".
C is really a measure of speed (d/t) equal to covering 1 planck length in 1 planck unit of time.
It's essentially the framerate of the universe, if like me you think of the Universe in terms of computation.
If you think of space and time as being discretized then C is exactly = 1.
So when you say C2 = M/E you are saying that mass and energy must add up to C2 which is 1 squared when everything is taken as planck units.
Another way of saying it, is that massless energy such as photons, will always travel at C.
So C = 1, then einstein could have written E = M period. Or if C is a constant, then he could have written
E = MK.
He was explaining an inertial effect. Exchanging momentum through time for momentum through space and vice versa. You need to add a concept of rate of change for that to work.