Motivated by applications such as on-device collaborative neural network inference, this work investigates edge-facilitated collaborative fog computing - in which edge-devices collaborate with each other and with the edge of the network to complete a processing task - to augment the computing capabilities of individual edge-devices while optimizing the collaboration for energy-efficiency. Collaborative computing is modeled using the Map-Reduce distributed computing framework, consisting in two rounds of computations separated by a communication phase. The computing load is optimally distributed among the edge-devices, taking into account their diversity in term of computing and communications capabilities. In addition, edge-devices local parameters such as CPU clock frequency and RF transmit power are also optimized for energy-efficiency. The corresponding optimization problem can be shown to be convex and optimality conditions can be obtained through Lagrange duality theory. A waterfilling-like interpretation for the size of the computing load assigned to each edge-device is given. Numerical experiments demonstrate the benefits of the proposed optimal collaborative-computing scheme over various other schemes in several respects. Most notably, the proposed scheme exhibits increased probability of successfully dealing with heavier computations and/or smaller latency along with energy-efficiency gains of up to two orders of magnitude. Both improvements come from the scheme ability to optimally leverage edge-devices diversity.