Distributed state estimation strongly depends on collaborative signal processing, which often requires excessive communication and computation to be executed on resource-constrained sensor nodes. To address this problem, we propose an event-triggered diffusion Kalman filter, which collects measurements and exchanges messages between nodes based on a local signal indicating the estimation error. On this basis, we develop an energy-aware state estimation algorithm that regulates the resource consumption in wireless networks and ensures the effectiveness of every consumed resource. The proposed algorithm does not require the nodes to share its local covariance matrices, and thereby allows considerably reducing the number of transmission messages. To confirm its efficiency, we apply the proposed algorithm to the distributed simultaneous localization and time synchronization problem and evaluate it on a physical testbed of a mobile quadrotor node and stationary custom ultra-wideband wireless devices. The obtained experimental results indicate that the proposed algorithm allows saving 86% of the communication overhead associated with the original diffusion Kalman filter while causing deterioration of performance by 16% only. We make the Matlab code and the real testing data available online.