This is how I did it:
7.23(1 + 0.0114)^x = 10
With x being the number of years.
Through trial and error: when x = 28, the population is 9.930723215 billion. 28 + 2014 (January 1st) = 2042 January 1st.
When x = 29, the population is 10.04393346 billion. 29 + 2014 (January 1st) = 2043 January 1st.
This means that on the 1st of January 2043, the population was OVER 10 billion. That means the population hit 10 billion sometime between the 28th and 29th year after 2014. So it's sometime in 2042.
X in the above equation is revealed to be 28.6133 (algebraically without trial and error), so it couldn't have been in 2043 when the population hit 10 billion because it's gone over by then. In fact if it's 28.6133 years after 2014, then it would be sometime in July of 2042, not 2043.