cosmology - Number density of photons and the total energy of the universe

I was reading over some assignment solutions that my lecturer put up and one of them said that instead of calculating the number of photons in the universe with the familiar method of $$\int^{\infty}_0(\tfrac{k_bT}{h})^3\tfrac{x^2dx}{e^x-1}\times \tfrac{8\pi}{c^3}.$$ That we can can take the mean energy of a photon to be $kT$ and use that as an estimate instead. He didn't go any further into explaining how to do so and I'm not sure I understand how to do what he meant.

Would it be something like $$n_{o,\gamma}=\tfrac{\text{Total energy density of universe}}{Energy one photon}?$$ If so then how does one calculate the total energy of the universe in this expression?