  Employing the Lagrange inverting series, a solution of the transcendental
equation $(x-a)(x-b)=le^{x}$, that can be considered a quadratic generalization
of the equation defining Lambert $W$ function, has been found in terms of
Bessel orthogonal polynomials. Once again a transcendental equation can be
formally solved by means of classic orthogonal polynomials, suggesting a link
between Rodrigues formulas and the terms of Lagrange series. A novel
representation for Bessel polynomials has been found, by means of differential
identity : $\left(x^{2}D\right)^{n}=x^{n+1}D^{n}x^{n-1}$
