In this paper, we study energy efficiency of an orthogonal frequency division multiplexing based system under power constraint and minimum rate requirement with system circuit power consideration. The optimal radio resource allocation is then formulated as an energy-efficient maximisation where we propose a novel low complexity solution for obtaining the optimal solution. The solution consists of the optimal source transmission power and its distribution among subcarriers. In spite of the iterative solution with high computational complexity in previous works, we propose a quickly convergent low complexity scheme based on solving a nonlinear logarithmic equation. To evaluate the accuracy of the proposed method, we compared its accuracy through simulations with the optimal solution in systems with and without circuit power consideration. Simulation studies indicate that the proposed method provide accurate solutions in both low and high signal to noise ratio regimes. The simulation results also indicate using our proposed method results in a significant improvement in the computational complexity.