This may have been asked before, but nonetheless I am unable to find it if so. We know Einstein's theory of relativity is confirmed experimentally, and so any postulations made in theory must be true.
I am having difficulty understanding why nothing can travel at the speed of light and yet photons can travel at the speed of light. From $E=mc^2$ we know that energy and mass are basically equivalent, and that the faster something travels the more mass it gains, thus at 99.999% the speed of light, it's mass is increased by a factor of 224, and at 99.9999999999% it's mass is increased by a factor more then 70,000, and at the speed of light it's mass is increased by a factor of infinity, and therefore would require an infinite amount of energy to push anything to the speed of light, thus making it impossible for anything to travel at the speed of light.
Now I know a photon is massless and this is why photons and gravitons (if they exist) are the exception to this rule, but it still carries energy, but if energy is equivalent to mass then how is it that a photon can travel at the speed of light? Does this not violate the very laws set forth in Special Relativity, or more likely, have I missed something very fundamental in the theory itself?