While the exactly words there will be a separation of church and state are not in the Constitution what we have are letters that show the intent of the founding fathers of this nation. We have Supreme Court rulings.
The 1st Amendment:
Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances.

Congress is the part of the government charged with law making and our Constitution clears states it will make no law. There is your wall, a metaphor and the religious in America keep wanting to tear down the wall.