The energydifference can be calculated by taking the massdifference and multiplying this with c^2.
This is used to calculate how energy you get when convert mass into energy, in a nuclear power station e.g.
In this situation E cannot be a constant because it depends on m. (or it depends on m*c^2, if you think that is a better way to say it)
The total amount of energy in a closed system is indeed constant. It can be calculated by bringing the system to full stop and then multiply the mass you have with c^2.
In this situation E still depends on m (or m*c^2), but now m is constant, just as E.