IMSO 2009 Mathematics — Taiwan Second Round Short Answer (20 Questions) Question 9

Each of the letters A, B, C, D, E is used to represent a single digit in these two statements. (Same letter = same digit.) $A+B=C$, $C+D=\overline{EA}$ (Note $\overline{EA}$ is a 2-digit number). What is the value of $B+D$?