Answer
$14$ years.
Work Step by Step
A difference is the result of subtraction.
$\left.\begin{array}{ccc}\text{(effect of lacking sleep)}&\text{minus}&\text{ (effect of smoking)}\\
-1&-&(-15)\end{array}\right.$
$-1-(-15)\qquad$subtract $-15$ by adding $15$, its additive opposite
$=-1+15\qquad$ use the rule for adding numbers of different signs
$=+14$
