I can use Filter-property with an integer or with a string but I can not
use a statement like

Table2.Filter:='Number=2 and Name='Joe''

What is the correct syntax for this statement?

Table2.Filter = Number = 2 and Name = ' + quotedStr('Joe');

I did a test on the DBDEMOS table customer.db and this filter worked:

Table1.Filtered := False;
    Table1.Filter := 'Addr2 = ' + QuotedStr('Suite 310') + ' and company = ' +
        quotedStr('Blue*') ;
    table1.Filtered := True;

and this as well

Table1.Filtered := False;
    Table1.Filter := 'Addr2 = ' + QuotedStr('Suite 310') + ' or company = ' +
        quotedStr('Blue*') ;
    table1.Filtered := True;

to prove that not only "and" will work but also "or".