  In this paper, we use the method of Thue and Siegel, based on explicit Pade
approximations to algebraic functions, to completely solve a family of quartic
Thue equations. From this result, we can also solve the diophantine equation in
the title. We prove that this equation has at most one solution in positive
integers when $d \geq 3$. Moreover, when such a solution exists, it is of the
form $(u,\sqrt{v})$ where $(u,v)$ is the fundamental solution of
$X^{2}+1=dY^{2}$.
