1. **Stating the problem:** We are given that Emma is $y$ years old, Hanna is 2 years older than Emma, and together their ages sum to 26 years. We need to write an equation for their combined age and solve for $y$. 2. **Writing expressions:** Hanna's age is $y + 2$. 3. **Forming the equation:** The sum of their ages is given by $$y + (y + 2) = 26$$ 4. **Simplifying the equation:** $$y + y + 2 = 26$$ $$2y + 2 = 26$$ 5. **Solving for $y$:** Subtract 2 from both sides: $$2y + \cancel{2} - \cancel{2} = 26 - 2$$ $$2y = 24$$ Divide both sides by 2: $$\frac{2y}{\cancel{2}} = \frac{24}{\cancel{2}}$$ $$y = 12$$ 6. **Finding Hanna's age:** $$y + 2 = 12 + 2 = 14$$ 7. **Answer:** Emma is 12 years old and Hanna is 14 years old.