Mark 1:1013 After his baptism, Jesus went to the desert where he was tempted
John 1:29 2:1 After his baptism, Jesus went to Cana in Galilee to attend a wedding
Aopparent contradictions in the Bible are basically always due to two mein reasons: A wrong understanding of what is written, or else a wrong translation from the old texts into our modern day languages. In this case with seemingly contradictory facts about what Jesus did immediately after his baptism by John in Jordan, the solution again is in reading carefully and accurately what is written in the gospel accounts and in understanding correctly what is mentioned there.
Mark 1:10-11 records without a doubt the baptism of Jesus in Jordan, and it mentions two further details which happened at the time of this baptism. For one, we read of the spirit descending like a dove on Jesus, furthermore we read of a voice from heaven which was directed to Jesus and in which God spoke to Jesus, "Thou are my beloved Son " Then follows an important detail in Verse 12: "And IMMEDIATELY the spirit driveth him into the wilderness". "IMMEDIATELY" is the keyword in this statement, for we are told that this happened right away, immediately, next in sequence, after the baptism of Jesus and the voice from heaven. "Immediately" leaves no extra time Jesus went right after this event under the direction of God by means of the spirit into the wilderness of Judea where he then was tempted. Verse 13 tells that the temptation lasted for 40 days.
The passage in John 1 must be read carefully as well because small details are of great importance for a correct understanding of this section of Scripture. Verse 29 mentions that Jesus "the next day" (i.e. the day following the events just mentioned in the verses before, when some of the Jews came to John questioning him) came to John. Then John the baptist mentions to the Jews which had come to him that this was the Jesus of whom he had spoken to them previously. In Verse 32 very important and decisive words are spoken by John which will help us put this section into its proper place and solve the apparent contradiction, because here it says of John, that he said, "I saw the Spirit descending from heaven like a dove, and it abode upon him." John speaks in the past tense, "I SAW ", when he reported what had happened at the baptism of Jesus. This day, when John was telling this to the Jews, was not the day when this had happened, but that day already had come and gone, this was already past. When we read the next few verses in John 1, we can recognize that some more days went by and that Jesus later left from there together with some new disciples who had been previously disciples of John, and he then went to a wedding in Cana in Galilee.
When we look at the two records now, we can gain the following overall picture of what happened:
At the baptism of Jesus by John in Jordan the spirit descended like a dove from heaven on Jesus and a voice came from heaven to Jesus in which God affirmed to him that he was God's beloved Son in whom his Father was well pleased. Immediately after this event Jesus went as directed by the spirit, into the wilderness of Judea and he remained there for a total of 40 days during which time he was tempted of the devil. John continued to baptize and many of the Jews came to him in order to be baptized, and John spoke to them about Jesus for whom he was sort of preparing the way. Then, at the end of those 40 days, when the temptation was over, Jesus came back to John near Jordan, on the day after John had had the discussion with the Jews as recorded in the previous verses in John, and now John reminded the Jews that it had been this Jesus of whom he had previously talked to them. He then mentioned also that God had testified to him that he would recognize Jesus as the spirit would descend like a dove from heaven and rest on him, and John says that this indeed had already happened. Jesus remained a few more days in this area where John continued to baptize, and he won a few new disciples from the disciples of John. These disciples then accompanied him a few days later when he left from this place near the Jordan in Judea to go to Galilee where he then went to attend a wedding at Cana.
This apparent contradiction is solved when we notice that the two records deal with events that happened at completely different times, and that the events recorded in John 1 occurred not until after the period of 40 days of temptation in the wilderness which are mentioned in Mark.