Answer
$\Delta E_{CD}=\Delta E_1-\Delta E_3$
Work Step by Step
$\Delta E_{CD}$ is the difference in energy between state C and state D.
According to the diagram
$E_C=E_A+\Delta E_1$
$E_D=E_A+\Delta E_3$
So
$\Delta E_{CD}=(E_A+\Delta E_1)-(E_A+\Delta E_3)$
$\Delta E_{CD}=E_A+\Delta E_1-E_A-\Delta E_3$
$\Delta E_{CD}=\Delta E_1-\Delta E_3$