The points $A$, $B$, $C$, $D$, and $E$ lie in one plane and have the following properties:

- $AB = 12$
- $BC = 50$
- $CD = 38$
- $AD = 100$
- $BE = 30$
- $CE = 40$

Find the length of the segment $ED$.

Let's think step by step and output the final answer within \boxed{}.
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