How to calculate the numbers of days between two dates in a query in base?

edit

It appears you are looking for the DATEDIFF function in HSQLDB v1.8. The documentation is available at this link, scroll down to the right place.

The function is summarized in the documentation as follows:

DATEDIFF(string, datetime1, datetime)

    returns the count of units of time elapsed from datetime1 to datetime2. 
    The string indicates the unit of time and can have the following values 'ms'='millisecond', 
    'ss'='second','mi'='minute','hh'='hour', 'dd'='day', 'mm'='month', 'yy' = 'year'. 
    Both the long and short form of the strings can be used.

Thus, in your case, the function you need probably would look something like the following:

SELECT DATEDIFF('dd', "DateArrived", "DatePurchase")
FROM "TableName"

The limitations of date functions in HSQLDB v 1.8 do cause headaches, for example see this question and answer, but this specific issue here seems quite solvable.