SOLUTION: What is the difference between the largest and smallest nine digit perfect square number(formed with 0,1,2,3,..,9 with no two digits repeating)

Question 1990: What is the difference between the largest and smallest nine digit perfect square number(formed with 0,1,2,3,..,9 with no two digits repeating)
Answer by longjonsilver(2297) (Show Source):
You can put this solution on YOUR website!
10,000 squared gives 100,000,000 --> the smallest 9 digit number
100,000 squared gives 1,000,000,000 --> 1 larger than the largest possible 9 digit number.
So our 2 numbers need to be between 10,000 and 100,000.
Now, i am not sure what you mean by "formed with"? Does this mean the number squared to give the answer has to be non-repeating or the number that is the result of the squaring has to be non-repeating.
I have assumed it is the original numbers, so...
smallest possible number is 10234.
largest possible number is 98765
98765^2 - 10234^2 = 9649790409
if it was the answers that were supposed to be non-repeating, then i have no idea how to do that algebraically. It would just be trial and error on my part. And i am NOT doing that :-)
jon.