The moment one enters into Prayer, he should pay attention to the fact that he is standing before His Creator. Consequently, he should not let anything occupy his mind other than Prayer. Sometimes, one becomes absent-minded to the extent that he may forget one of the obligatory or recommended acts of Prayer. Whenever such a thing happens, one should prostrate the two prostrations of forgetfulness known as sujud as-sahw. After sujud as-sahw there is no need to repeat the Tashahhud.

Sheikh Muhammed Salih Al-Munajjid states: There is no Tashahhud after sujud as-sahw, because the Messenger of Allah (peace and blessings be upon him) did not do that, as indicated in the Sunnah. If he had done that, he would have taught it to his Companions who, in turn, would narrate it. And he (peace and blessings be upon him) said: “Pray as you have seen me praying.”

Sheikh Ibn Qudamah said: Ibn Seereen and Ibn al-Mundhir said (concerning sujud as-sahw): There is Tasleem [termination of salah with “As-Salamu `alaykum” ] in them but there is no Tashahhud.

Ibn al-Mundhir added: The Tasleem (in sujud as-sahw) is proven from more than one chain of transmission, but there is some difference of opinion concerning the Tashahhud.
According to An-Nawawi, among the things we learn from the hadith of Dhul-Yadayn are:

Sujud as-sahw was done at the time of the Prophet (peace and blessings be upon him). That it consists of two prostrations, and that one should say Takbir (Allahu akbar) for each prostration. They are like the prostrations of Prayer, because they are called sujud, and if they had been different, he would have explained that. One should say Tasleem after doing sujud as-sahw, but there is no Tashahhud, and if one has to do sujud as-sahw because of doing something extra in the Prayer, this should be done after the Tasleem.