There are 2 arithmetic games which I need to solve but they are too hard. In the first one, you need to complete an equation by picking numbers from 1-9. The first levels are not that hard, but they get very hard as the game advances. Here is the link to the game:

https://www.novelgames.com/flashgames/game.php?id=83

Is there any program that would make me solve this game easy? Or perhaps an universal method?

The 2 game is similar only that you have 4 cards of different values, and you have to use this 4 cards and arithmetic signs to make a formula that gives 24. Ace is 1, Jack is 11, Queen is 12, King is 13. You have to use all 4 cards. Here is the link to this game:

https://www.novelgames.com/flashgames/game.php?id=73

As for the first game, there must be a program or method to solve this.

Any help would be greatly appreciated.

Now, to your questions. I believe there is no universal method to solving the two puzzles. A strategy can be developed and an algorithm can be implemented that would solve such problems programmatically. Whether it has been, i.e., whether there is a program does that does that I've no notion.

In passing, you may find interesting the following

https://www.cut-the-knot.org/Curriculum/Arithmetic/MakeIdentity/