In this article, we present an alternative moment generating function (MGF) based method for evaluating the receiver operating characteristics (ROC) of diversity energy detectors in a generalized fading environment. In contrast to the existing approaches that are based on either the circular contour integral and/or infinite series representations of the generalized Marcum Q-function Qu(.,.), we utilize an exponential-type integral for Qu(.,.) to facilitate the statistical averaging task over the independent and non-identically distributed (i.n.d) fading signal-to-noise ratios (SNRs). This leads to a very compact, exact, and an efficient solution for computing the average detection probabilities of diversity enabled energy detectors in a myriad of fading environments especially for the practical cases of square law selection (SLS) and square-law combining (SLC) diversity receivers with i.n.d and correlated fading statistics. Our unified analytical framework also encapsulates the existing results for Rayleigh, Nakagami-m, Nakagami-q and Rice fading environments by appropriate substitutions of the fading parameters in the κ-μ and η-μ generalized stochastic channel models.