Yes, there is such an equation, but it involves also the initial velocity, which is unknown, according to you. So the answer is uncertain without the initial velocity.
The equation itself is derived from the distance equation: $L(t)=L(0)+V_0\times t + F\times t^2/2m$. So your time is expressed via $D=L-L(0)$, $V_0$, and $F$. You just solve the square equation and find $t_{1,2}(D,V_0,F,m)$.