1. **State the problem:** Solve the equation $$\sqrt{x} + 2 = \sqrt{x} + 10$$. 2. **Analyze the equation:** We have the same term $$\sqrt{x}$$ on both sides of the equation. 3. **Subtract $$\sqrt{x}$$ from both sides:** $$\sqrt{x} + 2 - \sqrt{x} = \sqrt{x} + 10 - \sqrt{x}$$ $$\cancel{\sqrt{x}} + 2 - \cancel{\sqrt{x}} = \cancel{\sqrt{x}} + 10 - \cancel{\sqrt{x}}$$ which simplifies to $$2 = 10$$. 4. **Interpret the result:** The statement $$2 = 10$$ is false, which means there is no value of $$x$$ that satisfies the original equation. 5. **Conclusion:** The equation has **no solution**.