To find the integer that makes the subtraction sentence true, we can set up the equation as follows:
\[ -12 - x = -26 \]
To isolate \( x \), we can add \( x \) to both sides and also add 26 to both sides:
\[ -12 = -26 + x \]
This simplifies to:
\[ x = -12 + 26 \]
Calculating this gives:
\[ x = 14 \]
Thus, the integer that makes the subtraction sentence true is:
\[ \boxed{14} \]