Having no idea what the solution is how can you find the solute to get what the mystery solution is?

There is no way to be 100% sure what the solute is from the information given.  However, there are a few things you can do to narrow down the field of possibilities.

1) take a small sample of the solution and boil off the water, leaving the solid behind.  You want enough solid that you can collect three grain-sized samples.

2)  Do a Mel-Temp analysis on the solid.  If the solid melts at a relatively low temperature (under 300°C or so), then you can rule that the substance is most likely an organic compound.  If it melts above that temp, it's more likely ionic.

3) With anther solid sample, so a flame test to see what color of light is given off.  This will help identify what metallic elements, if any, are present in the compound.

4)  You can do a mass spec analysis on the third solid sample so you can get an approximation of the molar mass of the substance.

5)  You can use pH paper or a pH electrode to test the pH of the solution.  This will help determine if it is an acidic, basic, or neutral compound.

6)  You can do a precipitation analysis with small samples of the solution, testing it with compounds like silver nitrate or lead(II) nitrate.  This being done in hopes of precipitating out the anion, if it's an ionic compound, to tell what that ion is.

Those or my thoughts as to where you can go to start.