To find the value of \( x \), we can use the fact that angle \( E \) and angle \( B \) are corresponding angles formed when a transversal (the vertical line) intersects the two parallel lines (lines \( m \) and \( n \)). Since corresponding angles are congruent, we can set the measures of the two angles equal to each other:
\[ 3x + 18 = 14x - 8 \]
Now, let's solve for \( x \).
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Rearranging the equation: \[ 3x + 18 + 8 = 14x \] \[ 26 = 14x - 3x \] \[ 26 = 11x \]
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Divide both sides by 11: \[ x = \frac{26}{11} \]
The value of \( x \) is \( \frac{26}{11} \).
Thus, the answer is: \[ \frac{26}{11} \]