Let $r(b, t)$ denote the bitstring $b$ rotated to the left by $t$ bits: for example, $r(00110101, 5) = 10100110.$
Consider the following game. Player A picks two (different) $n$-bit strings $(T_1, T_2)$ and four arbitrary numbers $(a, b, c, d)$ less than $n$. Then Player A computes $$B_1 = r(T_1, a) \oplus r(T_2, b)$$ and $$B_2 = r(T_1, c) \oplus r(T_2, d),$$ then reveals $B_1$ and $B_2$ to Player B (we can assume that $B_1 \neq B_2$).
Given $B_1$ and $B_2$, how hard is it (in the average case) for the Player B to find two (different) $n$-bit strings $X_1$ and $X_2$ and four arbitrary numbers $(t, u, v, w)$ such that $$r(X_1, t) \oplus r(X_2, u) = B_1$$ and $$r(X_1, v) \oplus r(X_2, w) = B_2?$$