An integer of the form is called a Triangular number.

System of equations:

one solution is the pair

Find other pairs.

Paul found:

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An integer of the form is called a Triangular number.

System of equations:

one solution is the pair

Find other pairs.

Paul found:

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I think you may have mislabelled the resultant T values, 36 is T8 and 6 is T3.

Here are a few I found, with the first T number <500

T6 + T5 = 21 + 15 = 36 = T8 &

T6 – T5 = 21 – 15 = 6 = T3

T18 + T14 = 171 + 105 = 276 = T23 &

T18 – T14 = 171 – 105 = 66 = T11

T37 + T27 = 703 + 378 = 1081 = T46 &

T37 – T27 = 703 – 378 = 325 = T25

T44 + T39 = 990 + 780 = 1770 = T59 &

T44 – T39 = 990 – 780 = 210 = T20

T86 + T65 = 3741 + 2145 = 5886 = T108 &

T86 – T65 = 3741 – 2145 = 1596 = T56

T91 + T54 = 4186 + 1485 = 5671 = T106 &

T91 – T54 = 4186 – 1485 = 2701 = T73

T116 + T104 = 6786 + 5460 = 12246 = T156 &

T116 – T104 = 6786 – 5460 = 1326 = T51

T132 + T125 = 8778 + 7875 = 16653 = T182 &

T132 – T125 = 8778 – 7875 = 903 = T42

T247 + T242 = 30628 + 29403 = 60031 = T346 &

T247 – T242 = 30628 – 29403 = 1225 = T49

T278 + T209 = 38781 + 21945 = 60726 = T348 &

T278 – T209 = 38781 – 21945 = 16836 = T183

T392 + T374 = 77028 + 70125 = 147153 = T542 &

T392 – T374 = 77028 – 70125 = 6903 = T117

Paul.

Cool!