The minimum difference

Second digit in bigger number must be 0,and second digit in second number must be 9 and last three digits of the second number must be as big as they can so they are 876,last three number of bigger number must be 123 so 50123-49876=247 is solution...

Its instantly obvious the differance (n-m) between the first digits(n and m) must be 1, and the second digit should be 0 and 9 so that n0xxx-(m9xxx)=<1000.

This idea continued puts all the lowest availble numbers in acending order on the tail end of the higher number making the differance between n0000 and n0123 the lowest possible number. again the highest numbers in decending order should be applied to the lower number so that the difference Between n0000 and m9876 is the smallest possible. This leaves the consecutive numbers 4 and 5. So the solution is 50123-49876=247 (5000 being the midpoint)

Logic is take two consecutive numbers in 10000 place of bigger and small number.... We have minimisey difference so bigger number has small digits followed by and vice versa.....numbers are 50123 and 49876 gives diff 247