The goal of entity alignment (EA) is to discover equivalent entity pairs across different knowledge graphs (KGs), which is crucial for knowledge fusion and integration. Temporal knowledge graphs (TKGs) have gained increasing attention by extending traditional KGs with the introduction of timestamps. State-of-the-art studies on temporal-aware EA have demonstrated the benefits of incorporating temporal information from TKGs. However, we argue against the inclusion of both temporal and relational information in entity embeddings, as the temporal and relational information in most TKGs may interfere with each other, thereby limiting the performance. Therefore, we propose a Dual-task learning model for temporal knowledge graph entity alignment (DTTEA) that involves both a relational task and a temporal task. Firstly, the embeddings of both tasks are updated by optimizing a dynamic loss function. Then, a coarse-grained and a fine-grained similarity matrix are generated using the entity embeddings from two tasks as well as a temporal overlap matrix, which is then used for entity alignment. Extensive experiments on four real-world TKG datasets demonstrate that our proposed model outperforms state-of-the-art methods significantly. The code is available at https://github.com/w-oo/WORK/tree/master .