In general, battery-powered sensors in a sensor network are operable as long as they can communicate sensed data to a processing node. In this context, a sensor network has two competing objectives: (1) maximisation of the network performance with respect to the probability of successful search for a specified upper bound on the probability of false alarms, and (2) maximisation of the network's operable life. As both sensing and communication of data consume battery energy at the sensing nodes of the sensor network, judicious use of sensing power and communication power is needed to improve the lifetime of the sensor network. This paper presents an adaptive energy management policy that will optimally allocate the available energy between sensing and communication at each sensing node to maximise the network performance subject to specified constraints. Under the assumptions of fixed total energy allocation for a sensor network operating for a specified time period, the problem is reduced to synthesis of an optimal network topology that maximises the probability of successful search (of a target) over a surveillance region. In a two-stage optimisation, a genetic algorithm-based meta-heuristic search is first used to efficiently explore the global design space, and then a local pattern search algorithm is used for convergence to an optimal solution. The results of performance optimisation are generated on a simulation test bed to validate the proposed concept. Adaptation to energy variations across the network is shown to be manifested as a change in the optimal network topology by using sensing and communication models for underwater environment. The approximate Pareto-optimal surface is obtained as a trade-off between network lifetime and probability of successful search over the surveillance region.