The [Openstax Astronomy book](https://openstax.org/books/astronomy/pages/16-2-mass-energy-and-the-theory-of-relativity) talks about stars converting mass into energy via fusion reactions:

> So far, we seem to have a very attractive prescription for producing the energy emitted by the Sun: “roll” some nuclei together and join them via nuclear fusion. This will cause them to lose some of their mass, which then turns into energy.

It says that the amount of energy produced is described by the famous equation `𝐸=𝑚𝑐^2`, in which `c` is the speed of light.

My question is this (and maybe it's silly): does the speed of light *determine* the amount of energy released, or does it "just happen" to fit in this equation? In other words, if you could magically change the speed of light, would you thereby change the brightness of stars, or would this equation no longer be true?