Quantitative x-ray phase-contrast imaging requires solution of the phase-retrieval problem, that is the decomposition of the phase and amplitude of the x-ray wave from the intensity images. This generally requires measurement of at least two images with different object-to-detector distances. We propose a single-step phase-retrieval method that utilizes the dependence ofthe object's attenuation properties on x-ray energy. With this approach, the radiation dose delivered to the patient will be reduced significantly. This method relies on using a photon counting x-ray detector in conjunction with an x-ray source of sufficient lateral coherence. Intensity measurements are obtained for at least two energies at the detector end and the data is used in solving a transport of intensity equation (TIE) to obtain the electron density map and hence the phase-change due to the object. Being able to write down TIEs for more than one energy immediately simplifies the problem and enables new solution approaches. One such method as we have shown is by using two energy information, we can write down two TIE and solve them easily by decomposing the contribution of measured intensity into Compton scattering (C5) and Photoelectric (PE) effects. Thus we solve directly for projected electron density measurement which can yield projected phase change and differential phase change corresponding to any x-ray energy. We claim that other solution techniques and approximations are possible once TIEs are written down for two energies as proposed by our main claim. This approach has applications in soft tissue imaging like breast imaging and prostate imaging. The method is also envisioned to have applications in materials science and studies where electron density map of thick objects is required. This method will have applications in all phase retrieval methods using x-rays or other electromagnetic radiation. Other applications can be in x-ray imaging of luggage in baggage claims and detection of explosives using x-ray imaging. The method has shown to be working (through rigorous simulations) for thick tissue of several cms of thickness.