Let $G$ be a connected graph, $n$ the order of $G$, and $f$ (resp. $t$) the maximum order of an induced forest (resp. tree) in $G$. We show that $f-t$ is at most $n - \left \lceil 2 \sqrt{n-1} \right \rceil$. In the special case where $n$ is of the form $a^2+1$ for some even integer $a \geq 4$, $f-t$ is at most $n - \left \lceil 2 \sqrt{n-1} \right \rceil - 1$. We also prove that these bounds are tight. In addition, letting $\alpha$ denote the stability number of $G$, we show that $\alpha - t$ is at most $n + 1 - \left \lceil 2 \sqrt{2n}\right \rceil$; this bound is also tight.