Work it out with a few clues.
Only a 3 can be the last digit of number whose square has a 9 at the end.
There are 4 digits in the square, so the root is greater than 31, and less than 100.
The square of 5 = 25, so the square of 50 = 2500
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The squares of most 2 digit prime numbers. For example 2809, which is the square of 53, has 3 factors : 1, 53 and 2809 itself.
53 when multiplied by itself gives 2809.
No 38 is not a square number.
When you square a real number the answer is positive,
"Still" implies that the original number is a square number. In that case, the answer is as follows: There is no number such that it is a perfect sqiuare and that the number increased (or decreased) by 10 is also a perfect square. And if you do not limit it to perfect square then every non-negative number is a square with the number that is 10 more also being a square.