1. **State the problem:** Given that $HI = 10$ and $IE = x - 4$, find the value of $x$ and then find $IE$. 2. **Understand the relationship:** Since $HI$ and $IE$ are parts of a segment or related segments, and the problem implies equality or a relationship, we assume $HI = IE$. 3. **Set up the equation:** $$HI = IE$$ $$10 = x - 4$$ 4. **Solve for $x$:** Add 4 to both sides: $$10 + 4 = x - 4 + 4$$ $$14 = x$$ 5. **Find $IE$:** Substitute $x = 14$ into $IE = x - 4$: $$IE = 14 - 4 = 10$$ 6. **Conclusion:** The value of $x$ is $14$, and $IE$ equals $10$.