use time machine backup on another computer

If you connect the TM drive to the new Mac and hold down the Option key while accessing the TM menu in the menu bar you should get this:

Select the other Mac's TM drive, find the file you need and restore it.

No can do with Time Machine, if you attempt to do this you will ruin the Time Machine backup. Simply restore a copy of the file to the original machine, then copy that file to the new machine and you are done.