Traditional motion deblurring methods struggle to effectively model motion information within the exposure time. Recently, event cameras have attracted significant research interest for its ability to model motion cues over the exposure duration. However, these methods directly fuse event features with image, overlooking the intrinsic heterogeneity of events. In this paper, we identify that the event modality contains two conflicting types of information: edge features and motion cues. Events accumulated over a short exposure period capture sharp edge details but lose motion information, while those accumulated over a long exposure period blur edge details due to motion. To address this issue, we propose a simple yet effective approach to disentangle these two cues from event features and employ an edge-aware sharpening module along with motion-driven scale-adaptive deblurring module to fully leverage both. Specifically, the first module aids in restoring sharp edges by leveraging the clear edge features provided by events, while the second module leverages motion cues to learn diverse blur kernels, adaptively adjusting the receptive field for optimal deblurring. Extensive experiments on synthetic and real-world datasets validate the effectiveness of our approach and yield a substantial improvement over state-of-the-art single-frame methods and surpasses most multi-frame-based methods. Code will be publicly available.