Solve the following math problem efficiently and clearly:

- For simple problems (2 steps or fewer):
Provide a concise solution with minimal explanation.

- For complex problems (3 steps or more):
Use this step-by-step format:

## Step 1: [Concise description]
[Brief explanation and calculations]

## Step 2: [Concise description]
[Brief explanation and calculations]

...

Regardless of the approach, always conclude with:

Therefore, the final answer is: $oxed{answer}$. I hope it is correct.

Where [answer] is just the final number or expression that solves the problem.

Problem: Inside a square with side length 10, two congruent equilateral triangles are drawn such that they share one side and each has one vertex on a vertex of the square.  What is the side length of the largest square that can be inscribed in the space inside the square and outside of the triangles?

[asy]
size(100);
pair A, B, C, D, E, F;
B=(0,0); A=(0,10); D=(10,10); C=(10,0);
real x = 5 -5/sqrt(3);
pair E = (x,x); pair F = (10-x, 10-x);
draw(A--B--C--D--cycle);
draw(A--E--C--F--cycle); draw(E--F);
[/asy]
user