We calculate the energy gap (latent heat) and pressure gap between the hot and cold phases of the SU(3) gauge theory at the first order deconfining phase transition point. We perform simulations around the phase transition point with the lattice size in the temporal direction N-t = 6, 8 and 12 and extrapolate the results to the continuum limit. We also investigate the spatial volume dependence. The energy density and pressure are evaluated by the derivative method with nonperturabative anisotropy coefficients. We adopt a multipoint reweighting method to determine the anisotropy coefficients. We confirm that the anisotropy coefficients approach the perturbative values as N-t increases. We find that the pressure gap vanishes at all values of N-t when the nonperturbative anisotropy coefficients are used. The spatial volume dependence in the latent heat is found to be small on large lattices. Performing extrapolation to the continuum limit, we obtain Delta epsilon/T-4 = 0.75 +/- 0.17 and Delta(epsilon - 3p)/T-4 = 0.623 +/- 0.056.