For $\{T_n\}$ and $T$ positive and self-adjoint, show $T_n \stackrel{SR}{\to} T$ iff $(T_n + I)^{-1} \stackrel {s}{\to} (T + I)^{-1}$

Question

For $\{T_n\}$ and $T$ positive and self-adjoint, show $T_n \stackrel{SR}{\to} T$ (i.e. $T_n \to T$ in the strong resolvent sense) iff $(T_n + I)^{-1} \stackrel {s}{\to} (T + I)^{-1}$ (i.e. $(T_n + I)^{-1} \to (T + I)^{-1}$ strongly).

Not sure where to go with this one. I know that by definition $T_n \stackrel{SR}{\to} T$ if and only if $(\lambda I - T_n)^{-1} \stackrel {s}{\to} (\lambda I - T)^{-1}$ for $\lambda$ with $Im(\lambda) \neq 0$.

For the forward direction, I first thought it was trivial and that I could just use the special case $\lambda = 1$, but of course $Im(1) = 0$, so I can't.