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As recommender systems become increasingly sophisticated and complex, they often suffer from lack of fairness and transparency. Providing robust and unbiased explanations for recommendations has been drawing more and more attention as it can help address these issues and improve trustworthiness and informativeness of recommender systems. However, despite the fact that such explanations are generated for humans who respond more strongly to messages with appropriate emotions, there is a lack of consideration for emotions when generating explanations for recommendations. Current explanation generation models are found to exaggerate certain emotions without accurately capturing the underlying tone or the meaning. In this paper, we propose a novel method based on a multi-head transformer, called Emotion-aware Transformer for Explainable Recommendation (EmoTER), to generate more robust, fair, and emotion-enhanced explanations. To measure the linguistic quality and emotion fairness of the generated explanations, we adopt both automatic text metrics and human perceptions for evaluation. Experiments on three widely-used benchmark datasets with multiple evaluation metrics demonstrate that EmoTER consistently outperforms the existing state-of-the-art explanation generation models in terms of text quality, explainability, and consideration for fairness to emotion distribution. Implementation of EmoTER will be released as an open-source toolkit to support further research.