This Bible contradiction is from the Skeptic's Annotated Bible.

Verses

There was only one language.

Genesis 11:1 View context

And the whole earth was of one language, and of one speech.

Genesis 11:6-9 View context

And the LORD said, Behold, the people [is] one, and they have all one language; and this they begin to do: and now nothing will be restrained from them, which they have imagined to do.

Go to, let us go down, and there confound their language, that they may not understand one another's speech.

So the LORD scattered them abroad from thence upon the face of all the earth: and they left off to build the city.

Therefore is the name of it called Babel; because the LORD did there confound the language of all the earth: and from thence did the LORD scatter them abroad upon the face of all the earth.

There were many languages.

Genesis 10:5-31 View context

By these were the isles of the Gentiles divided in their lands; every one after his tongue, after their families, in their nations.

And the sons of Ham; Cush, and Mizraim, and Phut, and Canaan.

And the sons of Cush; Seba, and Havilah, and Sabtah, and Raamah, and Sabtecha: and the sons of Raamah; Sheba, and Dedan.

And Cush begat Nimrod: he began to be a mighty one in the earth.

He was a mighty hunter before the LORD: wherefore it is said, Even as Nimrod the mighty hunter before the LORD.

And the beginning of his kingdom was Babel, and Erech, and Accad, and Calneh, in the land of Shinar.

Out of that land went forth Asshur, and builded Nineveh, and the city Rehoboth, and Calah,

And Resen between Nineveh and Calah: the same [is] a great city.

And Mizraim begat Ludim, and Anamim, and Lehabim, and Naphtuhim,

And Pathrusim, and Casluhim, (out of whom came Philistim,) and Caphtorim.

And Canaan begat Sidon his firstborn, and Heth,

And the Jebusite, and the Amorite, and the Girgasite,

And the Hivite, and the Arkite, and the Sinite,

And the Arvadite, and the Zemarite, and the Hamathite: and afterward were the families of the Canaanites spread abroad.

And the border of the Canaanites was from Sidon, as thou comest to Gerar, unto Gaza; as thou goest, unto Sodom, and Gomorrah, and Admah, and Zeboim, even unto Lasha.

These [are] the sons of Ham, after their families, after their tongues, in their countries, [and] in their nations.

Unto Shem also, the father of all the children of Eber, the brother of Japheth the elder, even to him were [children] born.

The children of Shem; Elam, and Asshur, and Arphaxad, and Lud, and Aram.

And the children of Aram; Uz, and Hul, and Gether, and Mash.

And Arphaxad begat Salah; and Salah begat Eber.

And unto Eber were born two sons: the name of one [was] Peleg; for in his days was the earth divided; and his brother's name [was] Joktan.

And Joktan begat Almodad, and Sheleph, and Hazarmaveth, and Jerah,

And Hadoram, and Uzal, and Diklah,

And Obal, and Abimael, and Sheba,

And Ophir, and Havilah, and Jobab: all these [were] the sons of Joktan.

And their dwelling was from Mesha, as thou goest unto Sephar a mount of the east.

These [are] the sons of Shem, after their families, after their tongues, in their lands, after their nations.