Well, here is another:
Manipulate[
Grid[{
{"s(t):", First[sx /. Solve[0.20 == 0.266 - 0.032 sx + 0.00077 t, sx]]},
{"t(s):", First[tx /. Solve[0.20 == 0.266 - 0.032 s + 0.00077 tx, tx]]}
}],
{t, 10, 50, Appearance -> "Labeled"},
{s, 2.3, 3.3, Appearance -> "Labeled"}
]
Is this more like it?