Efficiency and equality are both important criteria when allocating public resources. Many previous studies have considered the trade-o_ between these two conflicting objectives. These studies have assumed that the manager of the resource has perfect information about participants' preferences. However, in many real applications, participants have private information and may behave strategically to benefit themselves. In this work, we consider the problem of allocating a set of homogenous resources (goods) between multiple strategic players while balancing both efficiency and equality from a game-theoretic perspective. We develop a general truthful mechanism framework for two very general classes of efficiency measures and equality measures which optimally maximize the resource holder's efficiency while guaranteeing certain equality levels. We characterize the optimal allocation rule fully, showing that there exists an optimal allocation where all the players can be divided into at most four groups and players in the same group have the same winning probability. Although there is no closed-form solution for the optimal allocation and truthful payments, we present polynomial-time algorithms to compute them. We also illustrate how the optimal efficiency changes for varying equality levels.