In this paper, a joint optimal allocation of transmit power at the source and jamming power at the destination is proposed to maximize the average secrecy energy efficiency (SEE) of a wireless network within a finite time duration. The destination transmits the jamming signal to improve secrecy by utilizing full-duplex capability. The source and destination both have energy harvesting (EH) capability with limited battery capacity. Due to the Markov nature of the system, the problem is formulated as a finite-horizon reinforcement learning (RL) problem. We propose the finite-horizon joint power allocation (FHJPA) algorithm for the finite-horizon RL problem and compare it with a low-complexity greedy algorithm (GA). An infinite-horizon joint power allocation (IHJPA) algorithm is also proposed for the corresponding infinite-horizon problem. A comparative analysis of these algorithms is carried out in terms of SEE, expected total transmitted secure bits, and computational complexity. The results show that the FHJPA algorithm outperforms the GA and IHJPA algorithms due to its appropriate modelling in finite horizon transmission. When the source node battery has sufficient energy, the GA can yield performance close to the FHJPA algorithm despite its low-complexity. When the transmission time horizon increases, the accuracy of the infinite-horizon model improves, resulting in a reduced performance gap between FHJPA and IHJPA algorithms. The computational time comparison shows that the FHJPA algorithm takes $16.6$ percent less time than the IHJPA algorithm.