We present the formulation of a novel integral-equation (IE)-based algorithm to solve for the scattered fields of a metasurface problem. The metasurface is assumed to be a thin sheet behaving according to the susceptibility model from the generalized sheet transition conditions (GSTCs). The proposed (implicit) IE-GSTC algorithm differs from other IE-GSTC methods by solving for the average scattered fields (by utilizing the mathematical properties of the IE operators) and only indirectly using the GSTC equations, which results in a reduced number of fundamental unknowns when compared to other methods. In addition, we show how the average scattered fields can be used in order to find the scattered fields everywhere. The proposed method is used to simulate two cases under the two-dimensional transverse-electric assumption. In particular, the results of the second case are compared to those obtained by a full-wave simulation in ANSYS HFSS.