Active and passive microwave remote sensing of snow have been studied with the same physical model of the Quasi-crystalline Approximation and the Dense Media Radiative Transfer (QCA-DMRT) Equation. The salient features of the model include a weaker frequency dependence and a stronger forward scattering than Rayleigh phase matrix for the same grain size. In this paper, we develop retrieval algorithms for snow water equivalent (SWE) based on the least square optimal estimate between the remote sensing data and the DMRT model. The retrieval algorithm is applied to passive satellite data from AMSR-E. The forest canopy is considered for mixed pixels. The passive retrieval algorithm makes use of the brightness temperatures of 18.7GHz and 36.5GHz. The snow grain size and snow depth are the two variables in the cost function. The retrieval algorithm has been applied to Alaska and to the Northwest regions of the United States. The results of retrieval algorithm are validated with SNOTEL ground measurement data from Natural Resources Conservation Service. The algorithm is shown to have better performance than the SSMI/AMSRE heritage algorithms. Retrieval algorithms of DMRT for active data from X- and Ku-band are also discussed.