The only way I found is: Use the definition of the hyperbola.

Let P denote any arbitrary point on the hyperbola. Then the equation must be true:

But I hope for you that the original question reads:

"Find the equation of the hyperbola if its focuses are and .

If so:

1. The center is at C(3, 2)

2. e = 13

3. From follows b = 5

4. The equation of the hyperbola is: .......