You didn't say which game, so I have no way of knowing. All the games with positive numbers are winnable. If you go to select game, you can try out four special games: -1 and -2 are unwinnable, and -3 and -4 will automatically win as soon as you make a move.

It is possible. I've done it myself, though its difficulty is another order of magnitude. I'm not going to give you a step-by-step, but here are a couple of hints:

Clear the left column first, ignoring the temptation in the right column.
Be prepared to move the 4 of diamonds in and out of cells a lot.
At one point, you'll have 3 hearts and 3 clubs cleared out before getting the other aces, but hearts first.