The airfoil integral equation over two disjoint intervals, separated by a distance $\kappa$, is considered. An analytic solution is obtained in terms of polynomials that satisfy a generalized three-term recurrence relation, particularly when utilizing a Chebyshev polynomial of the first kind as the input function. A new class of polynomials is defined on two disjoint intervals, demonstrating a generalization of a classical integral relationship previously established for Chebyshev polynomials on a single interval. The solutions are efficiently calculated, and comparisons with the original problem, defined on a continuous domain, are presented. Additionally, as $\kappa \rightarrow 0$, we derive approximate solutions for the Airfoil equation and exhibit the first terms of an asymptotic expansion of them in power series of $\kappa$ within weighted Sobolev spaces. The paper also outlines a spectral method for the general airfoil integral equation over two disjoint intervals.