Energy is not a thing. Energy is not a particle, it's not a force. Energy is a property of matter, kinda like color. Energy, being a property of matter, cannot have mass. It's like saying the color blue has mass. It makes no sense. Energy is a term that we use to describe a specific property of matter, and obeys certain conservation laws.
Conservation of Mass is not a universal law. The correct themodynamic law is conservation of Energy (1st law). Mass conservation only applies when you are dealing with classical physics, like balls colliding or chemistry. Mass conservation fails when you start dealing with relativity and nuclear reactions.
It is possible to change mass into energy. The atomic bomb, for instance, does just that. It takes some mass from the plutonium/uranium and converts that mass into energy which we then feel as 1) light 2) heat 3) shock waves. (Remember, we don't feel the energy directly, energy is a property of matter)
It is possible to convert energy into mass. A photon, which has no rest mass, of a high enough energy (say a gamma ray) can spontaneously convert itself into an electron/positron pair. This process is called pair production. Where you had zero rest mass before hand, you now have a mass of 2 Me (electron mass). Hence, we say that Mass Conservation is not a Universal Law, it's scope is limited to classical physics.
(well, I suppose you could use E=MC^2 to calculate the mass equivilance of all energy and say that mass is constant, instead of energy, but that would be silly and none in physics would do that.)
The statement E=MC^2 is an equivilance statement. X amount of energy is equal to Y amount of mass. It doesn't mean that energy has mass, or mass has energy (it's like saying Red has Shiny. It makes no sense). Mass and energy are both properties of matter. It simply means that these two properties are equivilant under certain contexts.
Edit: Positron, not proton. oops
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And if you say to me tomorrow, oh what fun it all would be.
Then what's to stop us, pretty baby. But What Is And What Should Never Be.
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