The #temp table isn't strictly necessary but may improve performance:

;WITH MassagedData AS (

SELECT Company,

MIN_Number = MIN(Number),

MAX_Number = MAX(Number),

rn = ROW_NUMBER() OVER(PARTITION BY Company ORDER BY MIN(Number))

FROM (

SELECT Company, Number,

gp = Number - ROW_NUMBER() OVER(PARTITION BY Company ORDER BY Number)

FROM #TransDetail

) d

GROUP BY Company, gp

)

SELECT a.Company, PriorNumber = a.MAX_Number, NextNumber = b.MIN_Number

INTO #RangeBoundaries

FROM MassagedData a

INNER JOIN MassagedData b

ON b.Company = a.Company AND b.rn = a.rn + 1

SELECT r.Company, p.[Site],

r.PriorNumber, PriorDate = p.TransDate, PriorTime = p.TransTime,

r.NextNumber, NextDate = n.TransDate, NextTime = n.TransTime

FROM #RangeBoundaries r

LEFT JOIN #TransDetail p ON p.Company = r.Company AND p.Number = r.PriorNumber

LEFT JOIN #TransDetail n ON n.Company = r.Company AND n.Number = r.NextNumber

ORDER BY r.Company, r.PriorNumber