**Given Information**

- The ratio of the sum and the difference of two numbers is 13:3.

**Let's assume**

Let's assume the two numbers as x and y.

**Ratio of the Sum and Difference**

According to the given information, the ratio of the sum and the difference of the two numbers can be expressed as:

(x + y) : (x - y) = 13:3

**Simplifying the Ratio**

To simplify the ratio, we can multiply both sides by the common factor of 3 and the denominator of the ratio (13 + 3 = 16):

3(x + y) : 3(x - y) = 13 : 3
3(x + y) = 13(x - y)

**Expanding the Equation**

Expanding the equation further:

3x + 3y = 13x - 13y

**Rearranging the Terms**

Rearranging the terms to isolate the variables:

16y = 10x

**Ratio of the Numbers**

Now, we can express the ratio of the two numbers x and y:

x : y = 16 : 10

**Simplifying the Ratio of the Numbers**

To simplify the ratio, we can divide both sides by the common factor of 2:

(x/8) : (y/5) = 1 : 1

Therefore, the ratio of the two numbers is 1:1.

**Conclusion**

The ratio of the sum and the difference of the two numbers is 13:3, and the ratio of the two numbers themselves is 1:1.

8:5