Does every topological $n$-manifold ($n>0$) admit an embedding into $\Bbb R^{2n}$? If not, what $n$-manifold does not embed into $\Bbb R^{2n}$?

Question

The strong Whitney Embedding Theorem tells us that every smooth n-manifold (n>0) admits a smooth embedding into $\mathbb{R}^{2n}$. Also, every topological $n$-manifold admits an embedding into $\mathbb{R}^{2n+1}$ (Munkres' Topology. Exercise §50.7).

My question now: can this last bound be lowered to $2n$? And if not, which topological $n$-manifold isn't embeddable into $\mathbb{R}^{2n}$? (Whitney's embedding theorem already tells us that such a manifold cannot admit a smooth structure)