According to my undergrad O chem book, t-butanol has a pKa of 17.8, 2-propanol 16.9, ethanol 15.9, methanol 15.5, and water 15.7.
Keq for the OP's reaction should be about 1/200 as written. In some cases you could entice the reaction to go in the forward direction by distilling away the product, but water's boiling point is higher than t-butanol's boiling point (82.2 degreesC), so that won't work. Unless you could add a dehydrating agent that won't interfere with the reaction to remove water from the solution, that is a useless reaction (as written).