Oracle analytic functions - how to get the highest RANKing row?
I fail to see the point of a requirements such as avoiding WHERE rank_ =, but here it is, without RANK(), or hardcoding a constant (still, hardcoding is done by using FIRST_VALUE):

select distinct grp,
  first_value(result1) over (partition by grp order by mbr desc) as result1,
  first_value(result2) over (partition by grp order by mbr desc) as result2
from (
select
  grp, mbr, 
  reading1 - lag(reading2) over (partition by grp order by mbr) result1,
  reading2 - lag(reading1) over (partition by grp order by mbr) result2
from (select unique grp, mbr,
             nvl(reading1, 0) as reading1, nvl(reading2, 0) as reading2
      from test)
);

GRP                 RESULT1    RESULT2
---------------- ---------- ----------
A                        -1        1.3
B                     -20.2      -20.4
C                      -100      100.3


When this is easier to read in my opinion:

select grp, result1, result2 from (
select
  grp,
  reading1 - lag(reading2) over (partition by grp order by mbr) result1,
  reading2 - lag(reading1) over (partition by grp order by mbr) result2,
  rank() over (partition by grp order by mbr desc) as rank_
from (select unique grp, mbr,
             nvl(reading1, 0) as reading1, nvl(reading2, 0) as reading2
      from test)
) where rank_ = 1
;