Link an ELF binary with a c program

Given only access to a standalone ELF program I want to be able to call a function within the program from my own program.Let's say the below code is main.c

#include <stdio.h>extern int mystery(int a,int b);int main() {        int a = 0;        int b = 1;        printf("mystery(a,b) = %d\n",mystery(a,b));        return 0;}

The function mystery exists in some elf file not_my_program.What I'm trying to do is something along the lines of

gcc main.c not_my_program

However this gives me an undefined reference error to mystery . I've looked for methods on forums and found that converting this elf file into a shared object file is not possible. I've also looked into compiling main.c into a relocatable object file with

gcc -c main.c

and then using ld to link the elf with main.o but I could not figure out how to do it. The elf is 32 bit but I've omitted the -m32 flag. If the flag is different for ld please let me know. Any help would be very much appreciated.

edit:output of readelf -h not_my_program

ELF Header:  Magic:   7f 45 4c 46 01 01 01 00 00 00 00 00 00 00 00 00   Class:                             ELF32  Data:                              2's complement, little endian  Version:                           1 (current)  OS/ABI:                            UNIX - System V  ABI Version:                       0  Type:                              DYN (Shared object file)  Machine:                           Intel 80386  Version:                           0x1  Entry point address:               0x10e0  Start of program headers:          52 (bytes into file)  Start of section headers:          15116 (bytes into file)  Flags:                             0x0  Size of this header:               52 (bytes)  Size of program headers:           32 (bytes)  Number of program headers:         11  Size of section headers:           40 (bytes)  Number of section headers:         30  Section header string table index: 29