Generating dual-energy subtraction (DES) soft-tissue images from chest radiographs (also called bone suppression) is an important task, as it improves the detection rates for lung nodules. Previous studies focus on generating DES-like soft-tissue images from CXRs through machine/deep learning techniques. However, they usually require tedious image processing steps for bone segmentation/delineation or ignore anatomical structure information (e.g., edges of ribs and clavicles) in CXRs. In this work, we propose a bone Edge-guided Generative Adversarial Network (EGAN) to generate DES-like soft-tissue images from conventional CXRs, which does not require human intervention and can explicitly use anatomical structure information of bones in CXRs. Specifically, the edges of ribs and clavicles in an input CXR were first detected by a trained fully convolutional network. Then, the edge probability map, as well as the original CXR image, are fed into a GAN model to generate the DES-like soft-tissue image, where the detected edge information is used as the prior knowledge to directly and specifically guide the image generation process. Experimental results on 504 subjects (each equipped with a CXR, a DES bone image, and a DES soft-tissue image) demonstrate that EGAN can produce DES-like soft-tissue images with high-quality and high-resolution, compared with classic deep learning methods. We further apply the trained EGAN to CXRs acquired by different types of X-ray machines in the public JSRT and NIH ChestXray 14 datasets, and our method can also produce visually appealing DES-like soft-tissue images.