Cryptogram Sum

Algebra Level 2

$\begin{array} { l l l } & A & B \\ + & C & D \\ \hline & E & F \\ \end{array}$

In the above cryptogram, all the letters represent distinct digits.

What is the minimum possible value of the 2-digit integer $\overline{EF}?$

Note: In cryptogram problems, 0 is not allowed to be a leading (first) digit, since we would just not write anything in its place.