Recognizing the pivotal role of EEG emotion recognition in the development of affective Brain-Computer Interfaces (aBCIs), considerable research efforts have been dedicated to this field. While prior methods have demonstrated success in intra-subject EEG emotion recognition, a critical challenge persists in addressing the style mismatch between EEG signals from the source domain (training data) and the target domain (test data). To tackle the significant inter-domain differences in cross-dataset EEG emotion recognition, this paper introduces an innovative solution known as the Emotional EEG Style Transfer Network (E$^2$STN). The primary objective of this network is to effectively capture content information from the source domain and the style characteristics from the target domain, enabling the reconstruction of stylized EEG emotion representations. These representations prove highly beneficial in enhancing cross-dataset discriminative prediction. Concretely, E$^2$STN consists of three key modules\textemdash transfer module, transfer evaluation module, and discriminative prediction module\textemdash which address the domain style transfer, transfer quality evaluation, and discriminative prediction, respectively. Extensive experiments demonstrate that E$^2$STN achieves state-of-the-art performance in cross-dataset EEG emotion recognition tasks.