I was going to comment this as well. Here is a thorough explanation of the missing term: https://physics.stackexchange.com/questions/143652/is-e2-mc2...
The thing that I love about this formulation of the equation is that it directly ties it to the Pythagorean theorem: c^2 = a^2 + b^2 . It really shows you just how pretty that equation really is!
the m in that equation is the rest mass (m_0) which is a proper scalar.
the m in E=mc^2 is the relativistic mass which depends on rest frame and therefore isn't a proper scalar quantity and that isn't a proper tensor equation.
the (E, px, py, pz) energy-momentum 4-vector is a tensor that transforms to any reference frame with a lorentz transform. all observers will agree on the shape of that 4-vector object, although they'll measure the components differently. that equation is just the dot product (rearranged), where the rest mass is the length of the 4-momentum vector (and a proper scalar quantity that all observers agree on is exactly that value in all reference frames). the rearrangement introduces a negative sign which actually comes from the SR metric -- usually diag(-1, +1, +1, +1) but sometimes diag(+1, -1, -1, -1).
E^2 = (mc^2)^2 + (lc)^2