1. **State the problem:** We are asked to find a number such that when 18 is added to it and then 15 is subtracted, the result is 22. 2. **Set up the equation:** Let the number be $x$. According to the problem, adding 18 and then subtracting 15 gives 22: $$x + 18 - 15 = 22$$ 3. **Simplify the equation:** Combine like terms on the left side: $$x + \cancel{18} - \cancel{15} = 22$$ $$x + 3 = 22$$ 4. **Solve for $x$:** Subtract 3 from both sides: $$x + 3 - 3 = 22 - 3$$ $$x = 19$$ 5. **Answer:** The number is $19$.