EMVA standard 1288 SNR formula (equation 11)
They have just substituted the statistics for shot noise back into the equation.
\$ \sigma_e^2 = \mu_e \$  and \$ \mu_e= \eta\mu_p    \$ i.e. # of electrons = QE * # photons and shot noise follows \$ \sqrt N \$ statistics.

Other than the different nomenclature (other than what I am used to that is) it is a good document and I recommend you conform to it's standards.