There is no contradiction my friend, the problem is people read them as if they are talking about the same time period.

Matthew talks about the childhood of Jesus when he would have been about 3 years old because Heros was unaliving babies 3 years and under, while Luke is talking about Jesus as a baby.

So they complement, not contradict each other.

If you however choose to read them as both talking about baby Jesus, then you start seeing contradictions everywhere.

Hope this helps.

Thanks again