The lens and source of the optical Einstein ring gravitational lens ER 0047-2808

(Abridged) We perform a detailed analysis of the optical gravitational lens ER 0047-2808 imaged with WFPC2 on the Hubble Space Telescope. Using software specifically designed for the analysis of resolved gravitational lens systems, we focus on how the image alone can constrain the mass distribution in the lens galaxy. We find the data are of sufficient quality to strongly constrain the lens model with no a priori assumptions about the source. Using a variety of mass models, we find statistically acceptable results for elliptical isothermal-like models with an Einstein radius of 1.17''. An elliptical power-law model (Sigma \propto R^-beta) for the surface mass density favours a slope slightly steeper than isothermal with beta = 1.08 +/- 0.03. Other models including a constant M/L, pure NFW halo and (surprisingly) an isothermal sphere with external shear are ruled out by the data. We find the galaxy light profile can only be fit with a Sersic plus point source model. The resulting total M/L_B contained within the images is 4.7 h_65 +/-0.3. In addition, we find the luminous matter is aligned with the total mass distribution within a few degrees. The source, reconstructed by the software, is revealed to have two bright regions, with an unresolved component inside the caustic and a resolved component straddling a fold caustic. The angular size of the entire source is approx. 0.1'' and its (unlensed) Lyman-alpha flux is 3 x 10^-17 erg/s/cm^2.