Explanation:

- Let's denote the two numbers as a and b.

- If the difference between two numbers ( a - b ) is greater than their sum ( a + b ), then:

 a - b > a + b

- Simplifying this, we get: b < 0

- Therefore, at least one number must be negative.

- Option 1: Both numbers being negative isn't necessary, as shown.

- Option 2: Exactly one negative number isn't sufficient as both can be negative.

- Option 3: At least one of the numbers is negative is correct.

- Option 4: This contradicts our findings.