This paper presents a novel fair scheme for resource sharing between nodes in OFDMA mesh networks. The problem is to maximize the overall system rate, under each user's maximal power and minimum rate constraints. To solve the underlying problem, we propose an approach that combines the merits of the well known Lagrange dual framework and the Lambert-W function. By using the Lambert-W function, resource allocation can not only be expressed in closed form but it can also quickly be determined without resorting to complex algorithms since a number of popular mathematical softwares, including Matlab, contain the Lambert-W function as an optimization component. Simulation results are provided to compare the performance of the proposed scheme with other allocation schemes.