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###Input checking

The most obvious issue that I see is that you are not verifying that the correct input is being entered. For example, if you enter a String instead of an int:

> hello
Exception in thread "main" java.util.InputMismatchException
  at java.util.Scanner.throwFor(Scanner.java:864)
  at java.util.Scanner.next(Scanner.java:1485)
  at java.util.Scanner.nextInt(Scanner.java:2117)
  at java.util.Scanner.nextInt(Scanner.java:2076)
  at Main.main(Main.java:8)

A natural way to do this is with Scanner.hasNextInt(). Also, consider adding a little bit of feedback so it is less confusing for the user. Something like this, for example:

    Scanner scan = new Scanner(System.in);
    int start;
    int end;
    
    System.out.println("Enter 1st whole number: ");
    while (!scan.hasNextInt()) {
        System.out.println("Input must be a whole number. Try again:");
        scan.next();
    }
    start = scan.nextInt();
    
    System.out.println("Enter 2nd whole number: ");
    while (!scan.hasNextInt()) {
        System.out.println("Input must be a whole number. Try again:");
        scan.next();
    }
    end = scan.nextInt();

Result:

Enter 1st whole number: 
> hello
Input must be a whole number. Try again:
> 5
Enter 2nd whole number: 
> world
Input must be a whole number. Try again:
> 20
5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

One other (more general) method (though it is more of an anti-pattern in this particular case) to validate things is with a try/catch block. See this answer on Stack Overflow for an example on how to do this.

    Scanner scan = new Scanner(System.in);
    int start;
    int end;
    
    try { 
        System.out.println("Enter 1st number:");
        start = scan.nextInt();
        System.out.println("Enter 2nd number:");
        end = scan.nextInt();

    } catch (java.util.InputMismatchException e) {
        System.out.println("Input must be an integer.");
        System.out.println("Exiting program.");
        return;
    }

Enter 1st number:
> hello
Input must be an integer.
Exiting program.

###Formatting

One other remark, although it is more stylistic, it is often considered a good habit in general to include braces in Java even when they are not needed. So this bit:

if(start < end)
    for(int i = start; i <= end; i++)
        System.out.print(i + " ");

else if(start > end)
    for(int i = start; i >= end; i--)
        System.out.print(i + " ");

Would look like this:

    if(start < end) {
        for(int i = start; i <= end; i++) {
            System.out.print(i + " ");
        }
    }
    else if(start > end) {
        for(int i = start; i >= end; i--) {
            System.out.print(i + " ");  
        }
    }