Triangle $DEF$ is shown.  What is $\cos{E}$?

[asy]
draw((0,0)--(7,0)--(7,24)--cycle,black+linewidth(1));
draw(rightanglemark((0,0),(7,0),(7,24),30),black+linewidth(1));
label("$E$",(7,24),E);
label("$F$",(0,0),W);
label("$D$",(7,0),E);
label("7",(0,0)--(7,0),S);
label("24",(7,0)--(7,24),E);
[/asy]
From the Pythagorean Theorem, we have $EF^2=DE^2+DF^2$, so \begin{align*}{EF}&=\sqrt{DE^2+DF^2} \\ &=\sqrt{24^2+7^2} \\ &=\sqrt{625} \\ &=25.\end{align*}Therefore, $\cos{E}=\frac{DE}{EF}=\boxed{\frac{24}{25}}$.