Synthesis of t-butyl ethyl ether is achievable via nucleophilic substitution using sodium ethoxide (C$_2$H$_5$ONa) and t-butyl chloride (C$_4$H$_9$Cl). Sodium ethoxide acts as a potent nucleophile, displacing the chlorine atom in t-butyl chloride to yield t-butyl ethyl ether. The reaction equation is: \[\text{C}_4\text{H}_9\text{Cl} + \text{C}_2\text{H}_5\text{ONa} \rightarrow \text{C}_4\text{H}_9\text{OC}_2\text{H}_5 + \text{NaCl}\] Therefore, t-butyl chloride and sodium ethoxide are the suitable reactants for this synthesis.