In this paper, minimax optimization problems involving (not necessarily) differentiable E-invex functions are considered. The sufficient optimality conditions for E-differentiable minimax optimization problems solving E-invex functions are established. To demonstrate the aforementioned results, an example of an E-minimax optimization problem is presented. The parametric and nonparametric Mond-Weir and Wolfe dual problems are formulated for the E-differentiable minimax optimization context. Furthermore, several duality theorems, including weak, strong, converse, and strict converse, are established under the assumptions of E-invexity.