Fog networks offer computing resources with varying capacities at different distances from end users. A Fog Node (FN) closer to the network edge may have less powerful computing resources compared to the cloud, but processing of computational tasks in an FN limits long-distance transmission. How should the tasks be distributed between fog and cloud nodes? We formulate a universal non-convex Mixed-Integer Nonlinear Programming (MINLP) problem minimizing task transmission- and processing-related energy with delay constraints to answer this question. It is transformed with Successive Convex Approximation (SCA) and decomposed using the primal and dual decomposition techniques. Two practical algorithms called Energy-EFFicient Resource Allocation (EEFFRA) and Low-Complexity (LC)-EEFFRA are proposed. They allow for successful distribution of network requests between FNs and the cloud in various scenarios significantly reducing the average energy cost and decreasing the number of computational requests with unmet delay requirements.