I was told that there is a problem and then its answer in each of Shakespeare's sonnet. What's the problem in sonnet 18?

All sonnets do this...the "turn" or the switch from problem or situation to answer is different for most sonnets.  Petrarchan or Italian sonnets usually "turn" after the first eight lines.  Sonnet 43 "How do I love thee" by Elizabeth Barrett Browning is one exception since her Italian sonnet begins to "turn" after the first line.

English sonnets--either Shakespearian or Spenserian (Edmund Spenser) turn after the first 12 lines.

I like to call the "turn" the BIG BUT.  The turn is usually begun with some transitional word or conjunction like yet, but, so, etc.

So, read your sonnet a min imum of 3 times.  First for the content--get the gist of the poem.  Second, for the problem and the solution (the turn is in there somewhere...look for the big but) Third for the rhythm and sheer beauty of the language. The more you read those 14 well-constructed lines, the better you'll understand them and the more you will learn to love poetry.

Good LUck!