A key challenge toward green communications is how to maximize energy efficiency by optimally allocating wireless resources in large-scale multiuser multicarrier orthogonal frequency-division multiple-access (OFDMA) systems. The quality-of-service (QoS)-constrained energy efficiency maximization problem is generally hard to solve due to the inverse transposition of the optimization operands in the optimization objective. We apply convex relaxation to make the problem quasiconcave with respect to power and concave with respect to the subcarrier indexing coefficients. The Karush-Kuhn-Tucker (KKT) optimality conditions lead to transcendental functions, where existing solutions are only numerically tractable. Different from the existing approaches, we apply the Maclaurin series expansion technique to transform the complex transcendental functions into simple polynomial expressions that allow us to obtain the global optimum in fast polynomial time, with the tractable upper bound of truncation error. With the new solution method, we propose a joint optimal allocation policy for both adaptive power and dynamic subcarrier allocations. We gain insight on the optimality, feasibility, and computational complexity of the joint optimal solution to show that the proposed scheme is theoretically and practically sound with fast convergence toward near-optimal solutions with an explicitly tractable truncation error. The simulation results confirm that the proposed scheme achieves a much higher energy efficiency performance with the guaranteed QoS and much lower complexity than existing approaches in the literature.