Pandas soustrait les jours de la date
df['date1'] = df['date'] - pd.to_timedelta(df['day'], unit='d')
print (df)
date day date1
0 2015-10-10 23 2015-09-17
1 2015-12-19 9 2015-12-10
2 2016-03-05 34 2016-01-31
3 2016-09-17 23 2016-08-25
4 2016-04-30 2 2016-04-28
Victorious Vicuña