Modern satellites deployed in low Earth orbit (LEO) accommodate processing payloads that can be exploited for edge computing. Furthermore, by implementing inter-satellite links, the LEO satellites in a constellation can route the data end-to-end (E2E). These capabilities can be exploited to greatly improve the current store-and-forward approaches in Earth surveillance systems. However, they give rise to an NP-hard problem of joint communication and edge computing resource management (RM). In this paper, we propose an algorithm that allows the satellites to select between computing the tasks at the edge or at a cloud server and to allocate an adequate power for communication. The overall objective is to minimize the energy consumption at the satellites while fulfilling specific service E2E latency constraints for the computing tasks. Experimental results show that our algorithm achieves energy savings of up to 18% when compared to the selected benchmarks with either 1) fixed edge computing decisions or 2) maximum power allocation.