The well-known adsorption integral equation (AIE) for calculating pore size and adsorption energy distributions from adsorption isotherms on porous solids is, from the mathematical point of view, a linear Fredholm integral equation of the first kind and therefore an ill-posed problem. What can we realistically expect from the solution of such an ill-posed problem by regularization? Does it make sense to restrict the number of possible solutions by the so-called ansatz method? In this paper, the two methods for solving ill-posed problems are from scratch explained and illuminated by concrete examples. Their relevance and fundamental limitations are discussed.