Is it true that a finite field extension with degree $>1$ cannot be isomorphic to its base field?

Question

Is it true that a finite field extension with degree $>1$ cannot be isomorphic to its base field?

Suppose two fields are isomorphic via the isomorphism $f: E \to F$. Then it is true that using $f$ as an embedding $[E:F] = 1$. However, there might still be other embeddings from $E$ to $F$. Are there any counterexamples of the statement?

Using the comment, let me consider $A= Q(2^{\frac{1}{4}})$ and $B = Q(2^{\frac{1}{2}})$. Apparently $B \subset A$. How to prove the other way around?