The total least squares (TLS) problem is studied for a special class of models that have the form of the inverse of a continuous one-to-one function. The parameters a and b to be found in a least squares sense appear through the argument ax + b to the inverse function. With TLS, there are significant errors in both the independent and the dependent variables, and the (possibly weighted) sum of the squares of the distances from the optimal fitting function and the data points is minimized. The formulation presented includes the exponential and generalized logistic models. A transformation is made to an equivalent nonlinear TLS problem that is linear in its parameters. This linearity is used to produce an effective algorithm whose iterations require solving an ordinary least squares problem and a system of nonlinear equations in which each equation has only one unknown. Existence and convergence theorems are provided, and the algorithm is demonstrated on a set of test problems. Following the theory requires a familiarity with real analysis; however, the algorithm description provides sufficient information for software developers who are less interested in the mathematical detail. The presentation is well done, and a good selection of references is provided.