An ORA-01722 ("invalid number") error occurs when an attempt is made to convert a character string into a number, and the string cannot be converted into a valid number.
Nls_date_format parameter helps to implicitly convert the varchar to a date type.
SQL>INSERT INTO tbl values ('01-02-16');
In the above example implicit type conversion happens since we have set
NLS_DATE_FORMAT . In your case it was trying to extract number(Or you could tell explicitly) from SYSDATE but found string not date.
SQL>SELECT SYSDATE-'01' FROM dual;
Here this works perfectly and returns the date subtracting 1 day from the SYSDATE because it was able to convert the string to number.
The best way is to explicitly convert the varchar to a date type.
You can use the following query to subtract date from sysdate(assuming you have set NLS_DATE_FORMAT=DD-MM-RR):
SQL>SELECT SYSDATE-TO_DATE ('01-01-01');
Oracle recommends to use explicit type conversion.