Autonomous unmanned aerial vehicles (UAVs) have become an important tool for efficient disaster response. Despite the virtues of UAVs in disaster response applications, various limitations (e.g., requiring manual input, finite battery life) hinder their mass adoption. In contrast, social sensing is emerging as a new sensing paradigm that utilizes signals provided by 'human sensors' to gather awareness of the events occurring in the physical world. Despite being inherently broader in scope, a shortcoming of social sensing is the reliability of the sensing data that are contributed by humans. In this paper, we introduce the concept of jointly exploiting the reliability of drones and the scope of social sensing to efficiently uncover the truthful events during disasters. However, such a tight integration of social and physical sensing introduces several technical challenges. The first challenge is satisfying the conflicting objectives of event coverage of the application and energy conservation of drones. The second challenge is adapting to the dynamics of the physical world and social media. In this paper, we present a Social-media-driven Energy-Aware Drone (SEAD) sensing framework to address the above challenges. In particular, we develop a reinforcement learning-based drone dispatching scheme that adapts to the physical and social environments and launches an appropriate proportion of drones for event exploration. We further utilize a bottom-up game-Theoretic task allocation approach to guide drones effectively to the event locations. The evaluation with a real-world disaster case study show that SEAD noticeably outperforms state-of-The-Art baselines in terms of detection effectiveness and energy efficiency.