However, the only known information is its daughter element (all relevant information of the daughter element can be obtained). Parent element's information is unknown.
Without Parent information, no way that I know of. You can use the "age equation" for the daughter obviously. But without the Parent AND Grandparent information, you can't use the "age equation" for the parent. As I'm sure you know, the information required for use of the "age equation" includes: D; number of atoms in the daughter today, P: number of atoms in the parent isotope today, and the appropriate decay constant from the table. If you wish to find the geologic age of the PARENT, you need to perform the same equation substituting Parent for daughter and Grandparent for Parent. So without both Parent and Grandparent isotopes' germane information, the geologic age of the parent can't be determined by any means I know of. Here is the age equation: But I'm sure you already know it.
t=1/λ ln (1+ D/P)
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