find $D$ of $(D+A)$ for $diag((D+A)^-1)=k$

Question

I am wondering whether it is possible to derive $D$ for

$diag((D+A)^{-1})=k$

where

• $diag()$ produces a vector of diagonal elements of a squared matrix,
• $D$ is an unknown diagonal matrix with possible values between zero and $\infty$, where it is known that $D$ exists,
• $A$ is a known positive definite symmetric matrix, and
• $k$ is a known vector of positive values between $>0$ and $diag(A^{-1})$

Thanks