Let's simplify the expression step by step:

((14-x)10 + x) / (x - (14-x)) = 14

First, distribute the 10 to (14-x) and simplify the numerator:

(140 - 10x + x) / (x - 14 + x) = 14

Combine like terms in the numerator:

(140 - 9x) / (2x - 14) = 14

Now, multiply both sides by (2x - 14) to get rid of the denominator:

140 - 9x = 14(2x - 14)

140 - 9x = 28x - 196

Add 9x to both sides:

140 = 37x - 196

Add 196 to both sides:

336 = 37x

Divide by 37:

x = 9.08

Therefore, the value of x that satisfies the equation is approximately 9.08.