The theory of the real interpolation method and the K-functional has been developed in several papers. There exists a close connection between the K-functional and the E-functional and, thus, between the corresponding K- and E-methods. By using these facts we can also obtain both new information about the E-functional (e.g. the E-divisibility in the Brudnyi-Krugljak sense and Holmstedt type formulas) and about the equivalence of the E- and K-spaces (e.g. reiteration and Wolff type theorems). In this paper we work in the opposite direction. Namely, we discuss and calculate directly the E-functional for some pairs of quasi-normed groups and, in particular, we also obtain some information about the K-functional. We point out several applications of our exact descriptions. In particular, we obtain some well-known exact formulas for the K-functional. Thus our results may also be regarded as a unification and generalization of some well-known exact descriptions both of E-functionals and of K-functionals.