No, you can’t. It only says the problem has a unique solution. It doesn’t even say an efficient algorithm for computing it exists, or even whether an algorithm exists. Neither of those are very hard to prove, but the theorem won’t help you there.

For comparison, let’s say the “sorting theorem” says “if you have n different numbers, you can place them in a sequence so that no number is larger than its predecessor”.

Now, you have two numbers. How do you apply that theorem to place them in a sequence so that no number is larger than its predecessor?