This is a question about the state of putting the try-catch inside the while.

public static void main(String[] args) {
    Scanner scanner = new Scanner(System.in);
    System.out.println ("Determine if the digit 10 and the digit 1 are the same."");
    System.out.println ("Enter 0 to stop";

    System.out.print("Enter a 2-digit integer from 10 to 99>>");
    Integer num = null;

    while (true) {
        try{
            num = scanner.nextInt();
        }catch(Exception e){
            System.out.print ("Invalid input". Please re-enter.>>");
        }finally {
            if (num == 0)
                break;
            else if ((num < 10) || (num > 99)) {
                System.out.print ("Not a two-digit integer") Please re-enter.>>");

            }else {
                if (num % 10 == num / 10) {
                    System.out.println ("Yes! 10 and 1 are equal");
                    System.out.print("Enter a 2-digit integer from 10 to 99>>");

                }else{
                    System.out.println ("No! 10 and 1 are different");
                    System.out.print("Enter a 2-digit integer from 10 to 99>>");
                }
            }
        }

    }
    scanner.close();
}