I read or saw an article somewhere stating that Einstein removed the minus sign "-" out of his equation to get E=mc2 to work. For the life of me, i still haven't found that article again. I might have a book somewhere that has that, but I have stuff in storage, it maybe in there.I agree ... different parts of theories get tweeked all the time ... we completely upended the Big Bang Theory recently ... but we're also confirming parts all the time ... and these parts stay put ...
What you're posting is the mathematical form of the Law of Conservation of Mass/Energy ... and in Modern Physics, there's no real distinction between mass and energy ... these two things we have from Classical Physics appear to be one in the same stuff ... and we have enourmous amounts of physical evidence to confirm the fact that mass and energy are different forms of the same stuff ... that this stuff is conserved ... and are interchangable by the ratio E = 10^16 m ... the 10^16 value has been determined in the lab ...
∂E/∂r = 2mc
∂m/∂r = -3E/c
That's not solvable so your guess is as good as mine ...
The only thing we know for sure on this earth is I think, therefore I am. You know we exist, anything past that is open to interpretation. So the current theory is the current interpretation to describe the world around us, that's basically science. If science says that theory "X" is fact, I treat it as a theory open to amendment because I think as a human race, we just know a tiny percentage of science. Maybe the things we see in Star Trek and other such sci fi films will become a reality. One day we might know what gravity is.