In this paper, a half-duplex two-way relay channel with energy harvesting nodes is considered. In particular, short-term throughput maximization problems are solved using a decode-and-forward relay. Necessary properties of the optimal transmission policy are derived to gain insights into the optimal solution. Then, a subgradient descent algorithm is used to find the optimal policy. It is observed through simulations that energy-deficient nodes act as bottlenecks on the achieved throughput. The achieved average throughput is observed to be close to the upper bound when nodes have no energy intermittency, and significantly higher than the throughput achieved by naïve policies.