Accurate boundary modelings that address the frequency-dependent sound absorption characteristics of various sound absorbers are crucial for wave-based room acoustic simulation. In time-domain simulations, however, a computationally demanding convolution appears in frequency-dependent impedance boundary conditions. The present paper proposes a room acoustic solver with a fourth-order accurate explicit TD-FEM, incorporating a frequency-dependent absorbing boundary condition efficiently using a recursive convolution method, namely the auxiliary differential equation (ADE) method. Its performance against the fourth-order accurate frequency-domain FEM is examined via 2D real-scale room acoustic problems, solving a sound propagation in an office room up to 4.5 kHz. Firstly, we describe briefly the formulation of the proposed room acoustics solver based on the explicit TD-FEM. Then, the discretization error property of the proposed method is evaluated via an impedance tube problem, including a frequency-dependent impedance boundary of porous sound absorber. Finally, the accuracy and efficiency of the proposed method are demonstrated with the comparison of frequency-domain FEM solver, which uses a sparse direct solver for the solution of the linear system at each frequency. Results showed the proposed method can perform an acoustic simulation with significantly low computational costs compared to the frequency-domain solver while keeping an acceptable level of accuracy.