Each number in the sequence is the sum of the term number and the number of letters in the spelt out version of the number.
Let the ith term of the sequence be denoted by S(i) and let the number of letters in the number i be T(i).
Then, S(i) = i + T(i)
S(11) = 11 + T(11) = 11 + 6 = 17 and
S(12) = 12+ T(12) = 12 + 6 = 18
Thus, the next two numbers are 17 and 18.