Second Stiefel-Whitney Class of a Five Manifold

Question

There is a unique rank 4 nontrivial orientable vector bundle over the 2-torus, denote this by $p:E\rightarrow T^2$. Denote the associated sphere bundle by $S(E)$. Then since $S(E)$ is orientable, the first Stiefel-Whitney class of the five manifold $S(E)$ is trivial. By Wu's formula, it's not hard to see that the second Stiefel-Whitney class $w_2(S(E))$ equals the second Wu class. But I have trouble in finding the second Wu class. Can anyone help me this out? Thanks!