A digit reversal

Let SS be the number obtained by writing all the numbers from 1 to 100 in order, and removing the spaces in between. Let TT be the number obtained by writing all the numbers from 1 to 100 in reverse order and removing the spaces in between.

What is the remainder when T2S2 T^2 - S^2 is divided by 1000 1000 ?

Details and assumptions

The number obtained by writing all the numbers from 1 to 10 in reverse order and removing the spaces in between, is 10987654321 10987654321.

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