The book of John does not relate the baptism of Jesus. It simply quotes John the Baptist talking about the baptism sometime after the fact. Nowhere does it claim to inform us of what happened immediately after Christ's baptism.
Matthew, Mark, and Luke all inform us that Jesus was led by the Holy Spirit into the wilderness after His baptism (Matthew 4:1; Mark 1:12; Luke 4:1), where He was to be tempted by the devil.
Since Matthew, Mark, and Luke are all in agreement about this, and since John does not say anything about it one way or another, I don't see how anything here can be called a contradiction.
The Council of Nicea (325 AD) had nothing to do with establishing which texts would be considered canonical, or in other words, included in the Bible. According to present historical records, the subject wasn't really even discussed. Rather, the Council of Nicea discussed the nature of Jesus Christ in response to the Arian controversy. By the end of their discussions the approximately 300 church leaders had reached near unanimous agreement on a Trinitarian view of the Son.
Further, from the time of the earliest extant documents that list various books as possible New Testament scriptures (the Muratorian Canon from around 200 AD) to the time when the New Testament canon was finally closed at the Councils of Hippo (393 AD) and Carthage (397 AD), only the following books appear to have ever been in serious question as to whether or not they should be included by the universal Christian church in the New Testament:
Revelation of John
The Shepherd of Hermas
Acts of Paul
Apocalypse of Peter
Epistle of Barnabas
Gospel of the Hebrews
Please note that this list is far from being "thousands" in length. Please also note that of all these disputed texts, only the Gospel of the Hebrews, which may have simply been an early Hebrew version of Matthew's Gospel, actually claims to present a historical record of the life and public ministry of Jesus Christ. The four gospels in our present New Testament (Matthew, Mark, Luke and John) have historically never been in doubt as to their standing as scripture by the universal Christian church.
Please also note that of these disputed texts, more were finally included than were excluded.
As you read the scriptures, do be careful not to misrepresent what they say. Misrepresenting them only confuses others and makes you look foolish.