[tex]E =\dfrac{1}{\sqrt 3+1} - \dfrac{1}{\sqrt[3]{9}+\sqrt[3]3+1} \\ \\ \\E = \dfrac{\sqrt 3-1}{(\sqrt 3+1)(\sqrt 3-1)} - \dfrac{\sqrt[3]{3}-1}{(\sqrt[3]{3}-1)(\sqrt[3]{9}+\sqrt[3]{3}+1)} \\\\ \\E = \dfrac{\sqrt 3 - 1}{(\sqrt{3})^2 - 1^2} - \dfrac{\sqrt[3]{3}-1}{(\sqrt[3]{3})^3-1^3}\\ \\\\ E = \dfrac{\sqrt 3 - 1}{2}-\dfrac{\sqrt[3]{3}-1}{2}\\ \\\\\Rightarrow \boxed{E = \dfrac{\sqrt 3 - \sqrt[3]3}{2}}[/tex]
