1/2Eo times ( (volume integral)E^2 dtau + (surface integral)E PHI da )
That's the equation, the first integral is over the voume of a surface charged (q) sphere of radius a > R (radius of sphere) so a Gaussian surface beyond the sphere and the second is over the surface, with E vector function and PHI scalr function are the field and potential of q.
I believe this sum would show the total electrostatic energy, since if a => infinity the surface integral goes to zero (as stated in my book) but I'm not 100% sure nor do I know how to show it is really more/less than the total if I'm wrong. If someone can tell me which it is and how to go about proving it I think I can take it from there, just don't know how to start. Thanks!
Yes, you are integrating energy density over volume. That is total energy.