This study presents a hybrid energy management system (EMS) for unmanned aerial vehicles (UAVs), integrating flexible photovoltaic (PV) panels with a high-capacity lithium-polymer (Li-Po) battery to enhance flight endurance and energy resilience. The proposed EMS features a multi-layered adaptive control architecture, combining fuzzy logic-based decision-making, short-term solar irradiance prediction using machine learning and closed-loop proportional-integral-derivative (PID) motor control. This architecture dynamically allocates power based on real-time solar irradiance, battery state of charge (SOC) and propulsion load. The approach aims to minimise battery stress while ensuring stable UAV operation under variable environmental conditions. Simulation results indicate that, without PV support, the UAV battery depletes in approximately 28 min. However, incorporating an 80 W PV panel extends the endurance to 37 min, and a 160 W effective PV configuration increases the flight time to over 50 min, while maintaining the SOC above 20%. This corresponds to a 79% improvement in endurance and nearly a 50% reduction in net battery energy consumption. The EMS effectively mitigates deep discharge cycles, improving battery health and operational lifespan. These findings demonstrate that the proposed hybrid EMS provides a scalable, adaptive and computationally efficient solution for balancing renewable and stored energy. It outperforms conventional static or single-source control strategies, particularly under fluctuating solar conditions.