Step 1: Let \( x^2 = A \) and \( y^2 = B \), so the two given conditions become \( A+B=3341 \) and \( A-B=891 \).
Step 2: For any two numbers whose sum and difference are known, the larger equals half the sum plus half the difference, and the smaller equals half the sum minus half the difference: \( A = \frac{3341+891}{2} = \frac{4232}{2}=2116 \), and \( B = \frac{3341-891}{2}=\frac{2450}{2}=1225 \).
Step 3: Taking square roots: \( x=\sqrt{2116}=46 \) and \( y=\sqrt{1225}=35 \).
\[ \boxed{35 \text{ and } 46} \]