The structure of core-shell micelles formed by nonionic surfactant Triton X-100 (TX-100) in a supercooled glucose-urea melt is investigated by contrast variation small-angle X-ray scattering (SAXS), small angle neutron scattering (SANS), and HR-TEM. Cooling a molten mixture of glucose-urea (weight ratio of 3:2) to room temperature yields a supercooled solvent without crystallization that can be used for trapping micelles of TX-100. By use of a combination of water and glucose-urea mixture at different proportions as solvent for micellization, the scattering length density (SLD) of the solvent can be tuned to match the shell contrast of the micelles. A systematic analysis of SAXS and SANS data with different SLD of solvent permits a quantitative evaluation of electron density profile of micelles in different matrices. The core of TX-100 micelles shows significant swelling in glucose-urea melt, as compared to that in water. The dimension and morphology of micelles were evaluated by scattering techniques and HR-TEM. Dynamic light scattering (DLS) studies suggest that, unlike micelles in water, the diffusion of micelles in supercooled glucose-urea melt decreased by several orders of magnitude.