Background: Monte Carlo (MC) methods are widely regarded as the gold standard for accurate dose calculations in radiotherapy treatment planning. However, their computational intensity often limits their practicality for complex intensity-modulated techniques in clinical workflows. Deterministic solvers based on the radiative transfer equation (RTE), which solve the linear Boltzmann transport equation (LBTE), have emerged as efficient alternatives for photon beam dose calculations, offering accuracy comparable to MC methods. To date, no RTE-based method has been fully developed for proton beam dose calculation. Objective: This work presents a novel RTE-based treatment planning method applicable to both proton and photon beams. By leveraging GPU acceleration, adaptive mesh methods, and techniques for solving the inverse problem, the proposed approach aims to provide high computational efficiency while maintaining accuracy. Method: The method eliminates the need for dose influence matrix construction in the optimization process by directly solving forward and backward RTE equations, avoiding large-scale matrix computations and iterative optimizations. The dose distribution is computed using a discrete numerical framework, combining multigroup energy discretization, Legendre expansion for angular discretization, and the discontinuous Galerkin (DG) method for spatial discretization. Adaptive refinements in spatial and angular resolutions further enhance computational performance. Result: Validation of the method was conducted by comparing dose distributions obtained with the proposed RTE-based solver against those from MC simulations with extensive particle histories. The results demonstrate excellent agreement, achieving gamma indices of 96.2% for a water tank case and 99.9% for a lung case. Conclusion: A novel RTE-based treatment planning method for both proton and photon beams has been developed, leveraging GPU acceleration and adaptive mesh refinement to achieve high computational efficiency while maintaining accuracy comparable to MC methods.