Numerical radius distance-preserving maps on $\mathcal{B}(H)$

Let $H$ be a complex Hilbert space, $\mathcal {B}(H)$ be the algebra of all bounded linear operators on $H$, $\mathcal {H}(H)$ be the subset of all selfadjoint operators in $\mathcal {B}(H)$ and $\mathcal{V}=\mathcal{B}(H)$ or ${\mathcal H}(H)$. Denote by $w(A)$ the numerical radius of $A\in\mathcal{B}(H)$. We characterize surjective maps $\Phi:{\mathcal V}\rightarrow{\mathcal V}$ that satisfy $w(\Phi (A)-\Phi (B))=w(A-B)$ for all $A,B\in{\mathcal V}$ without the linearity assumption.