Check the below input data and expected output to check the number is an Integer or not an Integer.

Input data: ‘1’

Expected Output:

IsInteger
--------------
An Integer

Input data: ‘8a’
Expected Output:

IsInteger
--------------
Not an Integer

Solution 1:

DECLARE @str AS VARCHAR(10) = '1'
SELECT 
	CASE WHEN SUM(CASE WHEN ASCII(t) BETWEEN 48 AND 57 THEN 1 END) = SUM(1) 
	THEN 'An Integer' ELSE 'Not an Integer' END IsInteger
FROM
(
    SELECT DISTINCT SUBSTRING(@str,Number,1) t
    FROM Master..Spt_Values
    WHERE Number > 0 AND Number <= DATALENGTH(@str)
)t1
GO

Solution 2: Using TRY_PARSE

DECLARE @str AS VARCHAR(10) = '8a'
IF TRY_PARSE(@str AS INT) IS NULL
    SELECT 'Not an Integer' AS IsInteger
ELSE
    SELECT 'An Integer' AS IsInteger
GO

Please try the different solution for this puzzle and share it via comment...