We work right to left when we add or subtract numbers. Therefore let's start the the #1# and #0# in both the numbers we're working with.

#=>=>1+0=1#

This number is in the ones place. No number changes are required.

#=>2+8=10#

Therefore the #1# of the #10# gets moved and raised to the next term we'll be dealing with. There zero of the #10# stays put in the tens place.

#=>3+6=9#

However, since we have that #1# from the #10#, we must add it to the #9#.

#=>=>9+1=10#

The zero will stay in the hundreds place, while the one moves to the thousands place.

Another #10# has been created. Therefore, do the same as above and move the #1# to the next part.

#=>2+1=3#

Once again, since we have that #1# from the #10#, we must add it to the number we're working with. This time it's #3#.

#=>=> 3+1=4#

We now can stop here since everything has been added properly. The #4# will remain in the thousands place permanently.

Therefore, the solution to #1,321+2,680=4,001#