Teaser 2863: Little time

From The Sunday Times, 6th August 2017 [link]

Do you have a little time to try this Teaser? I have taken a four-figure number and a six-figure number and I have consistently replaced digits by letters to give the words LITTLE and TIME.

If you take the digits of TIME and write down all the four-figure numbers which use exactly those digits in some order and then add up all those numbers, then your total will be LITTLE.

What number is TIME?