Colorectal cancer is one of the most prevalent cancers globally, and early detection of precancerous polyps is critical for preventing progression to malignant stages. To address the challenges in polyp segmentation, we propose TransE \(^2\) UNet, a novel deep learning-based architecture that integrates EfficientNet-B7 as the backbone encoder, Transformer, and Dilated Convolutions in the bottleneck, and Edge-Aware Attention Modules in the decoder. This combination enhances contextual learning, multi-scale feature extraction, boundary delineation, and computational efficiency. We evaluate TransE \(^2\) UNet on the Kvasir-SEG dataset, achieving a superior mean Intersection over Union of 0.9021 and mean Dice Similarity Coefficient of 0.9422, outperforming state-of-the-art methods. Additionally, we demonstrate the deployment potential of our approach by comparing it with several cross-domain datasets like BKAI-IGH and CVC-clinicDB. The superior performance in terms of standard metrics mIoU, mDSC, Precision, Recall, and F2 proves the efficiency of our method.