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The energy in E = mc^2 is the nuclear strong force or the force that holds protons and neutrons together in the nucleus of an atom. This is the energy that is released in nuclear reaction which give you the idea of the strength of that force.
The funny thing is, we have no idea how any of these forces (gravity, electromagnetic, strong, and weak) actually work. Gravity is atraction between two objects with mass. We have no idea why massive objects atract but we know they do. The electromagnetic force is an atraction between charged particles but we actually have no idea what this charge is and why it is like that. We call it positive and negative charge but it really means nothing. And those are the two forces we know the most about. As for the nuclear strong and weak forces, the weak force is actually the strong force ironically. The strong force holds the nucleus of an atom together and the weak force actually holds protons and neutrons together (the hold together the quarks that make up protons and neutrons).
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