Temperature raising elution fractionation (TREF) allows qualitative short chain branching (SCB) analysis in copolymers. In order to make the analysis quantitative, information on how such fractionation occurs must be incorporated into the interpretation of TREF spectra. In a previous work a model of the fractionation was proposed and some preliminary results given. In this article a rigorous mathematical analysis of the solution of the fractionation model is presented by defining two problems. The direct problem, of little practical use, helps to understand the fractionation process. The inverse problem consists in obtaining the distribution of crystallizable lengths (DCL) (directly related to the SCB distribution) from the TREF spectrum. This last problem (i.e., the main interest of this work) is explained in detail. TREF experiments are simulated solving the so-called direct problem using DCLs of different shapes. The synthetic TREF spectra are then processed using the inverse algorithm. The synthetic experiments demonstrate the adequacy of the proposed algorithm as a tool of analysis. A linear ethylene polymer was used to test, experimentally, the numerical procedure. The results obtained are in agreement with those obtained in earlier studies on the same sample by Raman spectroscopy.