In this paper presents an approximation for a trapezoidal type fuzzy number by a sequence of E-differentiable fuzzy numbers, i.e. fuzzy numbers with differentiable membership function in the interior of the E-level. The process consists on the construction of a differentiable fuzzy number using sup-min-convolution of a fuzzy number with a quasi-Gaussian fuzzy number. This work shows some numerical examples and a computational algorithm for this process.