Triangular Number Pairs with Triangular Sum and Difference

Theorem
The sequence of pairs of triangular numbers whose sum and difference are also both triangular begins:
 * $\left({15, 21}\right), \left({105, 171}\right), \left({378, 703}\right), \left({780, 990}\right), \left({1485, 4186}\right), \left({2145, 3741}\right), \left({5460, 6786}\right), \left({7875, 8778}\right)$