On rank-one corrections of complex symmetric matrices

Let a matrix $A\in M_n(\mathbf C)$ be a rank-one perturbation of a complex symmetric matrix, i.e. $A=X+Y$ for some unknown matrices $X$ and $Y$ such that $X=X^T$ and $\mathrm{rank}\,Y=1$. The problem of determining the matrices $X$ and $Y$ is solved.