for this you have to give the user admin rights.
for complete admin user equivalent as root you can do this
as root type command visudo for
remove # at line
## Same thing without a password
%wheel ALL=(ALL) NOPASSWD: ALL
save the file.
then modify user and add the user in group wheel
usermod -G wheel <user_name>
after this you can exicute root commands with sudo at start
sudo useradd <username>
if you want to give only adduser access to speicfic user than you have to see:
According to your requirments
for Solaris you have to study RBAC (roll bases access control)