x = 6.
Add the total length + the length outside of the circle and set it equal to the other segment’s total length + the length outside of the circle. Like this: (10+8)(8) = x(18 + x).
Then simplify to 144 = x^2 + 18x.
Use the quadratic formula (see picture), and x=6, x=-24. Except x ≠ -24 because the length cannot be a negative value. So x = 6!!
Here is a picture of my work:
I’m on my phone so it’s harder to type out the equations. Hope this helps!