Context. X-Shooter is the first second-generation instrument for the ESO-Very Large Telescope. It is a spectrograph covering the entire 300-2480 nm spectral range at once with a high resolving power. These properties enticed us to observe the well-known trans-Neptunian object (136199) Eris during the science verification of the instrument. The target has numerous absorption features in the optical and near-infrared domain that have been observed by different authors, showing differences in these features' positions and strengths. Aims: Besides testing the capabilities of X-Shooter to observe minor bodies, we attempt to constrain the existence of super-volatiles, e.g., CH4, CO and N2, and in particular we try to understand the physical-chemical state of the ices on Eris' surface. Methods: We observed Eris in the 300 - 2480 nm range and compared the newly obtained spectra with those available in the literature. We identified several absorption features, measured their positions and depth, and compare them with those of the reflectance of pure methane ice obtained from the optical constants of this ice at 30 K to study shifts in these features' positions and find a possible explanation for their origin. Results: We identify several absorption bands in the spectrum that are all consistent with the presence of CH4 ice. We do not identify bands related to N2 or CO. We measured the central wavelengths of the bands and compared to those measured in the spectrum of pure CH4 at 30 K finding variable spectral shifts. Conclusions: Based on these wavelength shifts, we confirm the presence of a dilution of CH4 in other ice on the surface of Eris and the presence of pure CH4 that is spatially segregated. The comparison of the centers and shapes of these bands with previous works suggests that the surface is heterogeneous. The absence of the 2160 nm band of N2 can be explained if the surface temperature is below 35.6 K, the transition temperature between the alpha and beta phases of this ice. Our results, including the reanalysis of data published elsewhere, point to a heterogeneous surface on Eris. Observations made during X-Shooter Science Verification, program 60.A-9400(A), PIs: Alvarez-Candal and Mason.