Learn Russian: Мы решим эту трудную задачу.

This is because the verb решить (to solve) is perfective, meaning it focuses on the successful completion of an action. Perfective verbs cannot happen in the present tense. When you add a present-tense ending like -им to a perfective verb, it automatically creates the simple future tense.

Why do the last three words end in -у and -ю (эту трудную задачу)?

They make up the direct object of the sentence—the thing being solved. This puts them in the accusative case. The basic feminine noun is задача (task), which changes its -а to -у. The describing words must match this feminine accusative form: эта (this) becomes эту, and трудная (difficult) becomes трудную.

What conjugation pattern does решим use?

The dictionary form is решить. It is a standard "Type 2" (or second conjugation) verb, which means it uses -и- in most of its endings instead of -е-. For example: я решу, ты решишь, and мы решим.

How would the sentence change if I wanted to say "we will be solving"?