Oblong numbers | O(a) + O(b) = O(c) – O(d)

An Oblong number is a number which is the product of two consecutive integers, that is, a number of the form   $n \,(n + 1)$

Let   $O_n \; = \; n \,(n + 1)$   be the n-th oblong number, for   $n \; = \; 1, \; 2, \; 3, \; ...$

Show that there are infinitely many pairs of distinct oblong numbers   $O_a, \; O_b$   and
$O_c, \; O_d$   with   $c > d$,   such that

$O_a \; + \; O_b \; = \; O_c \; - \; O_d$