Learn Russian: Я решу эту проблему завтра.

Решу is a perfective verb. Perfective verbs focus on the completed result of an action. Because you cannot complete a result in the ongoing present moment, adding normal present-tense endings to a perfective verb automatically makes it future tense! So, я решу means 'I will solve it and get it done.'

Why is it эту проблему instead of эта проблема?

The phrase 'this problem' is the direct object of the sentence, meaning it is the thing receiving the action of being solved. In Russian, we use the Accusative case for direct objects. For feminine words, the ending -а changes to -у. Therefore, эта проблема becomes эту проблему.

How would this sentence change if I used the imperfective verb решать?

If you used the imperfective verb, you would need the future helper verb буду (I will be). The sentence would become Я буду решать эту проблему завтра. That translates to 'I will be solving this problem tomorrow', focusing on the ongoing process. Our sentence uses the perfective решу because the speaker plans to actually finish the job.

Does завтра have to go at the end of the sentence?

Not at all! Russian word order is very flexible. Saying Завтра я решу эту проблему is completely natural and very common. Putting завтра at the end of the sentence just places a little extra spotlight on the timeframe.