Explainable recommendation is a good way to improve user satisfaction. However, explainable recommendation in dialogue is challenging since it has to handle natural language as both input and output. To tackle the challenge, this paper proposes a novel and practical task to explain evidences in recommending hotels given vague requests expressed freely in natural language. We decompose the process into two subtasks on hotel reviews: Evidence Identification and Evidence Explanation. The former predicts whether or not a sentence contains evidence that expresses why a given request is satisfied. The latter generates a recommendation sentence given a request and an evidence sentence. In order to address these subtasks, we build an Evidence-based Explanation dataset, which is the largest dataset for explaining evidences in recommending hotels for vague requests. The experimental results demonstrate that the BERT model can find evidence sentences with respect to various vague requests and that the LSTM-based model can generate recommendation sentences.