Step 1: Break the ether bond of \( (CH_3)_3C-O-C_2H_5 \) retrosynthetically into two possible ion pairs: (a) $(CH_3)_3C-O^-$ with $C_2H_5-Cl$, or (b) $C_2H_5-O^-$ with $(CH_3)_3C-Cl$.
Step 2: In every Williamson synthesis, the alkyl halide partner is the one that undergoes backside $S_N2$ attack, so its carbon must be as unhindered as possible. Compare the two halides: ethyl chloride has a primary carbon, while tert-butyl chloride has a tertiary carbon.
Step 3: A tertiary halide reacting with a small, strongly basic alkoxide such as ethoxide overwhelmingly undergoes E2 elimination instead of substitution, because the transition state for backside attack at a tertiary carbon is too crowded.
Step 4: Choosing pair (a), tert-butoxide (bulky base, fine as a nucleophile here) with ethyl chloride (primary, unhindered electrophile), removes this problem entirely, since substitution occurs at the primary carbon and elimination is not favored.
Step 5: This confirms that pair (a) is the workable combination for the synthesis.
\[ \boxed{(CH_3)_3C-O^- + C_2H_5Cl \rightarrow (CH_3)_3C-O-C_2H_5} \]